5G NR Beamforming — 3GPP Complete Reference

§1 — Beamforming Fundamentals

§1.1 — What is Beamforming?

Electromagnetic Wave Basics

An electromagnetic wave propagates at the speed of light \(c = 3\times10^8\) m/s. The relationship between frequency \(f\), wavelength \(\lambda\), and propagation speed is

At the 5G NR n78 carrier frequency of 3.5 GHz:

This wavelength underpins every dimension of a 5G massive-MIMO antenna panel — element spacing, aperture, and beam resolution are all expressed in multiples of \(\lambda\).

Antenna Gain Basics

Gain quantifies how much more power density an antenna delivers in its best direction compared with an isotropic radiator (0 dBi) that spreads power uniformly over a full sphere. A short dipole achieves approximately 2.15 dBi; a well-designed directive patch element reaches 10–25 dBi.

Coherent Superposition and Array Gain

When \(N\) antenna elements transmit the same signal with carefully chosen phase offsets, their E-fields add constructively in the desired direction and destructively in unwanted directions. The ideal (fully coherent) array gain over a single element is:

§1.2 — Wave Propagation & Phase Relationships

Inter-element Phase Difference

Consider two adjacent antenna elements separated by distance \(d\) along the x-axis. A plane wave arriving from angle \(\theta\) (measured from broadside, i.e. the normal to the array) travels an extra path length of \(d\sin\theta\) to reach the farther element. The resulting phase difference is:

For the standard 3GPP half-wavelength spacing \(d = \lambda/2\):

Array Factor (AF)

The combined radiation pattern for a uniform linear array of \(N\) elements with equal-amplitude weights is the Array Factor:

where \(w_n\) are the complex excitation weights (amplitude and phase) applied at the \(n\)-th element. For broadside steering with uniform weights \(w_n = 1/\sqrt{N}\), the maximum is \(\text{AF}_{\max} = N\).

Scan Loss

As the beam is steered away from broadside, the effective aperture seen by the incoming wavefront shrinks as \(\cos\theta\), and for a planar array the gain reduces approximately as:

Expressed in dB, the scan loss at angle \(\theta\) from broadside is:

Grating Lobes

Grating lobes are unwanted main-lobe replicas that appear in the array factor when the element spacing exceeds half a wavelength. They occur when the spatial phase difference equals a multiple of \(2\pi\):

For \(d = \lambda/2\): \(\sin\theta_{\text{GL}} = \pm 2\) — impossible since \(|\sin| \leq 1\). Therefore no grating lobes exist in visible space for \(d = \lambda/2\) across the full \(\pm 90°\) scan range. This is precisely why 3GPP specifies half-wavelength spacing for all NR massive-MIMO arrays.

§1.3 — 3GPP Antenna Element Model (TR 38.901 §7.3)

TR 38.901 defines a standardized single-element radiation pattern used in all 5G NR system-level simulations. The 3D element gain pattern combines horizontal and vertical envelope functions:

Horizontal Pattern

Vertical Pattern

Reference: 3GPP TR 38.901 Table 7.3-1 — Antenna element radiation pattern parameters for base station.

§1.4 — Antenna Polarization

Cross-Polarized (±45°) Design

Each physical TRX port in 5G NR massive-MIMO drives a cross-polarized element pair oriented at +45° and −45° to the vertical. The two orthogonal polarizations:

• Are physically co-located (same spatial position, different polarization axis), so they see identical path loss and large-scale fading.
• Experience largely uncorrelated small-scale fading, providing polarization diversity.
• Each carry an independent signal stream, enabling spatial multiplexing with just two physical antenna locations.

Polarization Isolation

The isolation between the two polarizations in a well-designed array exceeds 25 dB at boresight. This means leakage from the +45° port into the −45° receiver is at least 316× weaker in power — negligible for system performance.

Cross-Polar Discrimination (XPD)

In the propagation channel, the XPD ratio describes how much power couples from the intended polarization into the orthogonal polarization due to scattering. TR 38.901 UMa NLOS models XPD as a lognormal random variable:

The large spread (10 dB std dev) means the channel can temporarily collapse polarization orthogonality — a key consideration for MIMO rank adaptation.

§1 — Radiation Pattern: Array Factor vs Number of Elements

The chart below shows how the array factor narrows and strengthens as more antenna elements are added, for N = 1, 4, 8, and 32 elements with half-wavelength spacing and uniform weights steered to broadside.

§2 — Antenna Array Geometry

§2.1 — Uniform Linear Array (ULA)

The Uniform Linear Array (ULA) is the canonical one-dimensional array model: \(N\) identical elements placed along the x-axis with uniform inter-element spacing \(d\). All 5G NR beamforming theory starts here before extending to the 2D planar case.

Steering Vector

The response of an \(N\)-element ULA to a unit-amplitude plane wave arriving from angle \(\theta\) (from broadside) is captured by the complex steering vector \(\mathbf{a}(\theta) \in \mathbb{C}^N\):

The \(1/\sqrt{N}\) normalization ensures \(\|\mathbf{a}\| = 1\). When the beamforming weight vector \(\mathbf{w}\) is matched to the steering vector (i.e. \(\mathbf{w} = \mathbf{a}(\theta_0)\)), the received SNR equals \(N\) times the single-element SNR — this is the fundamental array gain.

3 dB Beamwidth

For a uniformly excited ULA, the half-power (3 dB) beamwidth is approximately:

For the horizontal dimension of the 32TRX reference system, \(N_H = 8\) and \(d = \lambda/2\):

§2.2 — Uniform Planar Array (UPA) — 3GPP 32TRX

The Uniform Planar Array extends the ULA concept to two dimensions: \(N_H\) elements horizontally and \(N_V\) elements vertically, enabling independent beam steering in both azimuth and elevation. 3GPP 5G NR systems universally use UPA topology for massive-MIMO panels.

32TRX Array Configuration

The reference 32TRX system has:

• \(N_H = 8\) horizontal antenna columns per polarization
• \(N_V = 4\) vertical antenna rows per polarization
• 2 polarizations (±45°) per physical location
• Total radiating elements: \(8 \times 4 \times 2 = 64\)
• Total TRX (transceiver) ports: \(8 \times 4 = 32\) (one port per dual-pol location)

2D Steering Vector — Kronecker Product

The 2D UPA steering vector for joint azimuth angle \(\phi\) and elevation angle \(\theta\) factorizes as a Kronecker product of the two 1D steering vectors:

where \(\mathbf{a}_H(\phi) \in \mathbb{C}^{N_H}\) and \(\mathbf{a}_V(\theta) \in \mathbb{C}^{N_V}\) are the horizontal and vertical ULA steering vectors respectively. This Kronecker separability is exact for an ideal planar array with identical element spacing in both dimensions.

Physical Dimensions at 3.5 GHz (\(\lambda = 85.7\) mm)

With half-wavelength spacing \(d_H = d_V = \lambda/2 = 42.86\) mm:

The active radiating aperture is therefore approximately 300 mm × 129 mm (30 cm × 13 cm), a compact form factor achievable on a standard macro BS mounting pipe. The full panel including radome and RF circuitry is typically ~500 mm × 300 mm × 100 mm.

Beamwidths and Gains

§2.3 — Array Size Comparison Table

The table below compares mainstream 5G NR massive-MIMO configurations. All figures assume \(d = \lambda/2\) spacing, 8 dBi single-element gain (TR 38.901 macro), and ideal coherent combining.

§2.4 — Near-Field vs Far-Field

Fraunhofer Distance

The boundary between the reactive near-field, radiating near-field (Fresnel), and far-field (Fraunhofer) regions is defined by the Fraunhofer distance:

where \(D\) is the largest physical dimension of the array aperture.

All outdoor macro UEs are well beyond 2.5 m from the base station, so standard far-field beamforming formulas apply without correction.

§2.5 — Grating Lobes Analysis

Grating Lobe Condition

Grating lobes are secondary main lobes of equal magnitude to the intended main lobe — not to be confused with sidelobes. They arise when the array samples the spatial frequency coarsely enough that there are multiple directions giving identical inter-element phase shifts. The condition for a grating lobe at scan angle \(\theta_0\) is:

For broadside steering (\(\theta_0 = 0\)), the first grating lobe appears at:

Scan-Dependent Grating Lobe Onset

When the beam is steered to angle \(\theta_0 \neq 0\), grating lobes can appear at lower spacing thresholds. The maximum spacing to guarantee grating-lobe-free operation across a scan range of \(|\theta| \leq \theta_{\max}\) is:

The 3GPP choice of \(d = \lambda/2 = 42.86\) mm at 3.5 GHz satisfies the most stringent case (\(\pm 90°\)), ensuring the panel remains free of grating lobes regardless of beamsteering direction.

§2 — 2D UPA Beam Pattern: 8×4 Array, d = λ/2, Boresight

The heatmap below shows the normalized 2D array factor (dB) for the 32TRX reference 8×4 UPA with half-wavelength spacing, steered to boresight (\(\phi = 0°\), \(\theta = 0°\)). The x-axis is azimuth angle \(\phi\) and the y-axis is elevation angle \(\theta\), both measured from broadside. The narrower horizontal beam (12.7°) vs vertical beam (25.4°) is clearly visible.

§3.1 — TR 38.901 Channel Model Overview

3GPP TR 38.901 ("Study on channel model for frequencies from 0.5 to 100 GHz") defines the authoritative propagation model used in all NR system-level simulations, including beamforming evaluations. Its foundation is a Geometry-Based Stochastic Channel Model (GSCM): rather than prescribing a fixed impulse response, the model generates random geometry (cluster positions, angles, delays) drawn from scenario-specific statistical distributions. This allows realistic spatial structure to emerge — structure that is crucial for evaluating how well a beamformer can exploit the channel.

The GSCM approach contrasts with the earlier SCM (3GPP TR 25.996) and WINNER models: TR 38.901 extends the frequency range to 100 GHz, introduces spatial consistency (nearby UEs see correlated channels), and adds blockage and oxygen absorption models for mmWave scenarios. For beamforming, the critical outputs of the model are the angle parameters that determine where energy arrives and departs at the array.

Key Angle Parameters

From TR 38.901 Table 7.5-6, the UMa NLOS scenario — the workhorse scenario for urban macro beamforming evaluations — has the following reference angle spread values: ASA ≈ 50°, ASD ≈ 12°, ZSA ≈ 10°, ZSD ≈ 9°. These values shape every system-level simulation result cited in NR beamforming whitepapers and standards evaluation reports.

§3.2 — Cluster Model for Beamforming

TR 38.901 models the propagation environment as a superposition of N_cl clusters, each representing a physical scattering region (building face, street canyon wall, ground reflection). For the UMa scenario, N_cl = 12 clusters for NLOS; each cluster contains M = 20 sub-rays with per-ray angular offsets drawn from a tabulated distribution.

The cluster model provides the structural link between physical scattering geometry and the beamforming opportunity: because each cluster has a dominant mean angle (φ_n, θ_n) with a finite angular spread, a beamformer can capture the cluster's power by steering within the cluster's angular extent. If the cluster has low intra-cluster spread, a narrow beam captures most of its power; if spread is large, a wider beam or multiple beams are needed.

The complete time-variant channel coefficient between transmit antenna element p and receive antenna element q, including both LOS and NLOS cluster components, is:

where:

• \(K_R\) is the Rician K-factor (power ratio of LOS to NLOS component; K_R = 0 for pure NLOS)
• \(P_n\) is the cluster power (drawn from an exponential power delay profile with per-cluster shadowing)
• \(\mathbf{F}_{rx,q}, \mathbf{F}_{tx,p}\) are the 2×1 field pattern vectors (H-pol, V-pol) of receive element q and transmit element p respectively, evaluated at the cluster's AoA/ZoA and AoD/ZoD
• \(\phi_{n,m}\) is the initial random phase of sub-ray m in cluster n, drawn uniformly from [0, 2π) per polarisation component
• \(f_{n,m} = v\cos(\alpha_{n,m}-\alpha_v)/\lambda\) is the Doppler frequency of sub-ray m, where \(\alpha_v\) is the UE travel direction

§3.3 — UMa, UMi, RMa Angle Statistics

TR 38.901 Table 7.5-6 tabulates the log-normal distribution parameters (mean μ, standard deviation σ) for each angle spread parameter across deployment scenarios. The table below gives the mean values (μ in degrees, or K-factor in dB for LOS) that are used in system-level beamforming simulations. These are the values that directly constrain achievable beamforming gain and spatial multiplexing capacity in each environment.

Source: 3GPP TR 38.901 v17.0.0, Table 7.5-6 — Stochastic parameters for channel generation in UMa, UMi-Street Canyon, and RMa scenarios. Values shown are μ of the log-normal distribution for angle spreads; all in degrees.

§3.4 — Impact of Angle Spread on Beamforming

Angle spreads are not merely descriptive parameters — they directly determine how many spatial degrees of freedom the channel offers a beamformer, and hence the maximum achievable spatial multiplexing gain. The intuition is as follows: if all energy arrives from a single direction (zero spread), one beam captures everything. As spread grows, energy is distributed across many spatial directions, and a single beam captures only a fraction of the total power.

Effective Spatial Rank from Angle Spread

A practical rule of thumb for estimating how many independent spatial streams the channel supports (its effective rank) comes from comparing the ASA to the array's azimuth beamwidth. For a linear array with N elements at half-wavelength spacing, the 3dB azimuth beamwidth at broadside is approximately:

The effective rank is then estimated as the number of beamwidths that fit within the azimuth spread:

For a 32TRX array configured as 8×4 (N_H = 8 horizontal elements per polarisation), BW_3dB ≈ 51°/8 ≈ 12.7°. Applying the formula:

§3.5 — Doppler and Time-Varying Angles

In the TR 38.901 GSCM, UE mobility causes the AoA/AoD to evolve over time as the UE moves relative to the scatterer clusters. From the UE's perspective, a scatterer at distance r appears to move in azimuth at angular rate dφ/dt = v·sin(φ)/r. At vehicular speeds and short cluster distances, this angular variation can be significant enough to make a fixed beam mispointed within one subframe.

The associated Doppler frequency for a plane wave arriving from angle φ relative to the UE velocity vector is:

At v = 120 km/h (33.3 m/s), f_c = 3.5 GHz (λ = 0.0857 m), the maximum Doppler shift occurs at φ = 0° (scatterer directly ahead of UE travel):

The channel coherence time — the interval over which the channel can be considered approximately static for beamforming purposes — is:

At numerology μ = 1 (SCS = 30 kHz), one NR slot is 0.5 ms. Therefore, at 120 km/h, the beam must be updated every ≈ 2 slots to maintain coherent beamforming. This has direct implications for beam management overhead:

[1] 3GPP TR 38.901 v17.0.0 — Study on channel model for frequencies from 0.5 to 100 GHz. 3GPP RAN WG1, 2022. §7.5 cluster-based channel model; Table 7.5-6 angle spread parameters; §7.6 special scenarios (HST, indoor, O2I).

§4.1 — ULA Steering Vector (Derivation from First Principles)

The steering vector is the fundamental mathematical object in array signal processing: it encodes how a plane wave from a particular direction appears across the antenna elements of an array. All beamforming operations — whether analogue phase shifting, digital precoding, or codebook selection — ultimately amount to designing a weight vector whose inner product with the steering vector maximises received (or transmitted) signal energy in a desired direction.

Consider a Uniform Linear Array (ULA) of N isotropic antenna elements, spaced d apart along the x-axis. A plane wave arrives from angle θ measured from broadside (the perpendicular to the array axis). The signal path-length difference between element n (at position x_n = n·d) and the reference element (n=0) is:

The corresponding phase difference (relative to element 0) is:

where the spatial frequency \(u = 2\pi d \sin\theta / \lambda\) captures the full angular-to-phase mapping. The normalised steering vector is then:

Note the normalisation by \(1/\sqrt{N}\) so that \(\|\mathbf{a}(\theta)\|^2 = 1\) regardless of array size. At broadside (θ = 0°), sin θ = 0, so u = 0 and:

All elements contribute in phase — this is the maximum constructive interference condition. The receive signal after matched filtering with the steering vector is:

The signal power is preserved (|\(\mathbf{a}^H\mathbf{a}\)| = 1 by normalisation), while the noise power is reduced from \(N\sigma_n^2\) (summing N noise terms incoherently) to \(\sigma_n^2\) (coherent combining cancels noise variance by N):

This N-fold SNR improvement is the array gain of coherent beamforming — the fundamental benefit that drives the deployment of large antenna arrays in 5G NR.

§4.2 — UPA Steering Vector for 3GPP 32TRX

Practical 5G gNB arrays are not ULAs but Uniform Planar Arrays (UPAs), arranged on a 2D grid to enable both azimuth and elevation beamforming simultaneously. The 32TRX reference configuration is an 8×4 UPA (N_H = 8 horizontal elements, N_V = 4 vertical elements, per polarisation), or equivalently described as an 8×2 panel with cross-polarised elements.

Element (m, n) is located at position (m·d_H, n·d_V) in the horizontal-vertical plane, where m = 0, …, N_H−1 and n = 0, …, N_V−1. For a plane wave from azimuth φ and zenith elevation θ (measured from zenith, so θ = 90° is horizon):

The horizontal phase increment (per horizontal element index m):

The vertical phase increment (per vertical element index n):

The 2D steering vector is formed as a Kronecker product of the 1D vertical and horizontal steering vectors:

where:

• \(\mathbf{a}_H(\phi,\theta) = [1, e^{j\psi_H}, e^{j2\psi_H}, \ldots, e^{j(N_H-1)\psi_H}]^T\) — N_H-element horizontal steering vector
• \(\mathbf{a}_V(\theta) = [1, e^{j\psi_V}, e^{j2\psi_V}, \ldots, e^{j(N_V-1)\psi_V}]^T\) — N_V-element vertical steering vector
• The Kronecker product ⊗ maps to the full N_HN_V-element array vector

Separability and Computational Efficiency

The Kronecker structure has a crucial computational advantage: a 2D beam can be implemented as two sequential 1D operations. Rather than searching a 2D grid of N_H×N_V combinations, the beamformer can first search N_H horizontal beams independently (horizontal beam sweep), then refine N_V vertical beams — reducing complexity from O(N_H·N_V) to O(N_H + N_V). For a 64-element array (8×8), this reduces beam sweep candidates from 64×64 = 4096 to 8+8 = 16, a 256× reduction. This is the architectural principle behind the 3GPP two-stage beam management (P1 for broad horizontal sweep, P2/P3 for vertical refinement).

§4.3 — Array Gain Formula

The coherent beamforming gain from an N-element array is:

For 32 TRX ports (the baseline massive MIMO configuration for Sub-6 GHz NR):

The total effective isotropic radiated power (EIRP) in the steered direction is the sum of transmitter output power, antenna element gain, and array gain:

For a typical 32TRX Active Antenna Unit (AAU) with 200 W total output power (P_TX = 53 dBm), 8 dBi element gain (typical patch element in a 3GPP-compliant 32TRX module), and 15.05 dB array gain:

Each doubling of TRX count adds 3 dB array gain, following the logarithmic law. The diminishing returns in EIRP per additional port make 32–64 TRX the practical sweet spot for Sub-6 GHz deployments: beyond 64 TRX, the hardware cost (additional PA chains, ADC/DAC, fronthaul bandwidth) grows linearly while the EIRP gain grows only logarithmically.

§4.4 — Beamsteering Weight Computation

Given a desired steering direction (φ₀, θ₀), the optimal transmit weight vector (maximising EIRP in that direction under total power constraint ||w||² = 1) is the conjugate of the steering vector:

This is the matched filter result: the beamformer aligns the phase of each element's contribution to coherently sum at the desired direction. For analogue beamforming, each element's phase shifter is set to −ψ_H,m − ψ_V,n, cancelling the propagation phase to achieve coherent combining.

DFT-Based Codebook (Type I, TS 38.214)

In practice, the gNB cannot steer to an arbitrary continuous angle — it selects from a finite codebook. The 3GPP Type I single-panel codebook (TS 38.214 §5.2.2.2) uses a DFT grid with oversampling factors O₁ and O₂:

The (l, m) DFT beam in the codebook has horizontal spatial frequency:

The quantisation loss from mapping continuous angle to the nearest DFT grid point is, for the worst-case (mid-point between two DFT beams):

For N₁O₁ = 32 (8 elements, O₁=4): ΔG_quant = −10 log₁₀(cos²(π/64)) ≈ 0.06 dB — negligible. Even with O₁=1 (no oversampling, N=8 beams): ΔG_quant ≈ 0.91 dB. This confirms that 4× oversampling (the 3GPP standard) effectively eliminates quantisation loss as a practical concern.

§4.5 — Null Steering

Beamforming does not only amplify signals in desired directions — it can also deliberately suppress signals from interfering directions by placing nulls. This is exploited in MU-MIMO to prevent one UE's beam from interfering with co-scheduled UEs, and in interference rejection combining to suppress dominant interferers.

Given a desired steering direction θ₀ and a required null at θ_null, the null-steered weight vector is formed by projecting out the null-direction component:

This projection ensures \(\mathbf{a}^H(\theta_{\text{null}})\,\mathbf{w}_{\text{null}} = 0\), i.e., zero array response at the null direction. For N antenna ports, the array has N−1 complex degrees of freedom (after normalisation), meaning up to N−1 independent nulls can be placed simultaneously. For a 32-port array:

• 31 independent nulls available — one degree of freedom per port after the main beam is fixed
• For 16-layer MU-MIMO: the gNB places 16 steering directions (one per UE) plus up to 15 nulls toward each co-scheduled UE's direction from each of the 16 beams — requiring careful precoder design to balance gain vs. null depth
• In practice, ZFBF (Zero-Forcing BeamForming) and its regularised variant RZF (Regularised Zero-Forcing) are used in 5G NR gNBs as a computationally tractable approximation to placing simultaneous nulls toward all interfered UEs

§4.6 — Polarimetric Beamforming

All 5G NR massive MIMO arrays are dual-polarised (±45° cross-pol or H/V polarisation). Each physical antenna panel contains twice as many radiating elements as TRX ports — each spatial position has one H-pol and one V-pol element, each connected to its own TRX chain. For a 32TRX configuration:

• 16 physical antenna positions (e.g., 8×2 grid)
• × 2 polarisations = 32 TRX ports
• H-pol beamformer weight vector: w_H ∈ ℂ¹⁶
• V-pol beamformer weight vector: w_V ∈ ℂ¹⁶

The total received electric field at the UE (ignoring path loss) is:

where h_H, h_V ∈ ℂ¹⁶ are the H-pol and V-pol channel vectors between the array and the UE. This gives the gNB two independent sets of 16 complex weights to optimise — a richer beamforming space than a single-pol array.

Key benefits of dual-polarisation in beamforming:

[2] 3GPP TS 38.214 v17.3.0 — NR; Physical layer procedures for data. §5.2.2.2 Type I single-panel codebook; oversampling factors O₁, O₂; W1×W2 precoder structure. 3GPP RAN WG1, 2022.

[3] 3GPP TS 38.211 v17.3.0 — NR; Physical channels and modulation. §7.3.1.4 reference signal port mapping; UPA element ordering; DM-RS antenna port definitions. 3GPP RAN WG1, 2022.

[4] T. L. Marzetta et al., Fundamentals of Massive MIMO. Cambridge University Press, 2016. Ch. 2: ULA/UPA steering vectors; Ch. 4: zero-forcing beamforming; Ch. 5: pilot contamination and multicell considerations.

§5   3GPP Codebook: Type I & Type II

§5.1   Codebook Design Philosophy

A codebook is a pre-agreed, finite set of precoding matrices jointly known to gNB and UE. Instead of feeding back the full channel matrix H ∈ ℂ^N_r×P, the UE searches this set, selects the entry that maximises throughput, and reports only the index — the Precoding Matrix Indicator (PMI). The gNB then applies that matrix for PDSCH transmission.

Two Codebook Families in TS 38.214 §5.2.2

Factored Precoder Structure: W = W1 × W2

Both Type I and Type II share a two-stage factored structure that decouples wideband beam group selection from fine-grained co-phasing and beam combination:

• W₁ — wideband, slowly varying. Selects a beam group of DFT steering vectors from the N₁×N₂ antenna grid. Reported once per wideband (or long period).
• W₂ — subband, faster varying. Selects beams within the group and applies cross-polarisation co-phasing. Reported per subband (≈8 PRBs).

3GPP TS 38.214 §5.2.2 — CSI codebook definition and PMI reporting framework. Normative for NR Rel-15 onwards.

§5.2   Type I Single-Panel Codebook

The Type I single-panel codebook (TS 38.214 §5.2.2.2.1) targets deployments with a single planar antenna array of N₁ horizontal and N₂ vertical dual-polarised ports. For a 32TRX panel: N₁ = 8 (horizontal), N₂ = 4 (vertical), giving 32 physical ports per polarisation.

DFT Oversampling Grid

The codebook oversamples the antenna array's DFT space with factors O₁ (horizontal) and O₂ (vertical), both defaulting to 4. The resulting beam grid dimensions are:

Each of the 512 candidate DFT beams is a unit-norm complex steering vector. Only a small subset (the selected W₁ group) is ever reported in a given measurement instant.

W1 Beam Group Selection

W₁ selects a 2×L block of beams (L = 1, 2 or 4 per polarisation group, configured by RRC parameter codebookType). For rank-1 transmission L = 1, giving a single beam pair (one per cross-polarisation group). The beam group index i₁ is reported wideband and consumes ⌈log₂(O₁N₁/2 × O₂N₂/2)⌉ = 4 bits (for 32TRX, L=1).

Rank-1 Precoding Matrix

where v_l ∈ ℂ^N₁N₂ is the l-th 2D DFT beam vector (defined in §5.3), the factor 1/√(2N₁N₂) normalises transmit power, and φ_n ∈ {1, j, −1, −j} is the cross-polarisation co-phasing coefficient reported via the W₂ index i₂ (2 bits for rank-1).

PMI Overhead Summary — Rank-1, 32TRX

3GPP TS 38.214 §5.2.2.2.1 — Type I single-panel codebook. Tables 5.2.2.2.1-1 through 5.2.2.2.1-12 define codebook entries for all ranks.

§5.3   Type I DFT Beam Grid — Key Equations

The 2D DFT beam vector for a dual-polarised panel is formed as a Kronecker product of independent horizontal and vertical steering vectors.

Horizontal Steering Vector

Vertical Steering Vector

2D Beam Vector (Kronecker)

Beam Pointing Angles

Beam index (l₁, l₂) steers to discrete angles in the sin-space representation:

For N₁ = 8, O₁ = 4: 32 discrete azimuth beams, beam spacing = 1/32 in sin(φ_H). For N₂ = 4, O₂ = 4: 16 discrete elevation beams, beam spacing = 1/16 in sin(θ_V). Both axes cover sin ∈ [−1, 1] fully, with uniform angular sampling density.

§5.4   Type II Codebook

Type II (TS 38.214 §5.2.2.2.3) abandons the single dominant-beam assumption. Instead, it superimposes L DFT beams with per-subband complex amplitude coefficients, capturing multi-path contributions from several angular directions simultaneously.

Type II Precoder Construction

where B is the wideband beam basis (same L beams across all subbands) and C^(f) ∈ ℂ^L×r contains the per-subband complex amplitude coefficients for subband f. The index f indexes subbands (each ≈ 8 PRBs in a 100 MHz carrier), with up to N₃ = 13 subbands for a 132-PRB allocation.

PMI Overhead Comparison

3GPP TS 38.214 §5.2.2.2.3 — Type II CSI codebook. Rel-15; enhanced in Rel-16 (§5.2.2.2.5).

§5.5   Enhanced Type II — Rel-16 Frequency-Domain Compression

Release 16 (TS 38.214 §5.2.2.2.5) introduced the enhanced Type II codebook, whose key innovation is frequency-domain (FD) compression of the subband coefficient matrix C^(f).

FD Compression Principle

Across N₃ subbands, the L×r coefficient matrix varies smoothly (the channel has limited frequency selectivity relative to subband spacing). This variation can be expressed in a compressed DFT basis over the subband dimension:

where f_m ∈ ℂ^N₃ is the m-th DFT basis vector over the subband grid, and α_l,r,m is the complex amplitude for beam l, layer r, FD basis m. With M << N₃, the coefficient set reduces from L × r × N₃ to L × r × M complex values.

Compression Ratio and Gain

3GPP TS 38.214 §5.2.2.2.5 — Enhanced Type II CSI codebook (Rel-16). FD basis vectors from a length-N₃ DFT codebook.

§5.6   Rank vs PMI vs RI Summary Table — 32TRX

The following table summarises Type I codebook feedback overhead for a 32TRX panel (N₁=8, N₂=4, O₁=O₂=4, 13 subbands). Actual bit counts follow TS 38.214 Table 5.2.2.2.1-x structures.

Note: actual bit-field widths depend on N₁, N₂, O₁, O₂, L, and rank configuration. See TS 38.214 Tables 5.2.2.2.1-1 through 5.2.2.2.1-12 for the full normative encoding.

Type I DFT Beam Grid Visualisation — 32TRX (N₁=8, N₂=4)

Each dot represents one DFT beam direction in sin(φ_H) vs sin(θ_V) space. The highlighted rectangle is an example W₁ beam group; the four coloured markers within it show selected L=4 beams (i₁ group at l₁=8, l₂=4).

The Type I codebook provides the quantized beam grid that the gNB applies as a precoding matrix W to the PDSCH signal. → §6 details how W is applied in the baseband signal chain and how BFWs are transported in O-RAN split 7-2x.

§6   Baseband Precoding: How gNB Applies W

§6.1   Baseband Signal Chain for Precoded PDSCH

This section traces the per-slot processing pipeline from encoded bits to precoded antenna-port signals for a 32TRX, 16-layer downlink transmission (maximum MU-MIMO capacity). The chain follows TS 38.211 §7.3.1.

Step-by-Step Processing (TS 38.211 §7.3.1)

3GPP TS 38.211 §7.3.1 — Physical downlink shared channel processing. §7.3.1.3 layer mapping; §7.3.1.4 antenna port precoding.

§6.2   Precoding Matrix W for 16-Layer MU-MIMO

A single UE is limited to 8 layers (2 codewords × 4 layers each) in NR Rel-15. Achieving 16 simultaneous spatial layers requires at least 2 UEs scheduled on the same time-frequency resource — this is Multi-User MIMO (MU-MIMO).

MU-MIMO Precoder Design

Let UE k have channel matrix H_k ∈ ℂ^N_r×P. The gNB forms UE-specific precoders W_k to simultaneously serve K UEs:

The second term is inter-user interference (IUI). Null-steering precoders suppress IUI by projecting each UE's precoder into the null space of the other users' channels. The ideal condition is:

SVD-based Null-Steering

The gNB computes the SVD of the combined interferer channel H_k,⊥ = [H_j]_j≠k and projects W_k onto its null space:

16-Layer MU-MIMO Configurations (32TRX)

§6.3   DMRS Port Assignment for 32TRX / 16 Layers

Demodulation Reference Signals (DMRS) must be orthogonal across layers so the UE can estimate each layer's effective channel independently. For 16 layers, the DMRS multiplexing capacity of a single OFDM symbol (12 ports maximum with DMRS Type 2) is insufficient — a multi-symbol DMRS configuration is required.

DMRS Type 2 Capacity

3GPP TS 38.211 §7.4.1.1 — DMRS for PDSCH. Table 7.4.1.1.2-1: DMRS port configurations for ν = 1…12 per OFDM symbol (Type 2, CDM groups 0–2).

DMRS Port-to-Layer Mapping

§6.4   Frequency-Selective Precoding (Subband PMI)

With a Type II codebook, the UE reports a separate W^(f) per subband. The gNB applies a different precoding matrix for each subband group, tracking the frequency-selective variation of the channel — particularly important in rich multipath environments where delay spread exceeds several OFDM symbol durations.

Implementation Architecture

• OFDM-domain precoding: W is applied in the frequency domain before the per-port IFFT. Each subcarrier k within subband f receives weight matrix W^(f). No time-domain filtering required.
• Subband grouping: for 132 PRBs at 30 kHz SCS, split into N₃ = 13 subbands of ~8–10 PRBs each (TS 38.214 Table 5.2.1.4-2).
• Computational cost (32TRX, 16 layers, 132 PRBs): complex multiplications per OFDM symbol = P × ν × N_SC = 32 × 16 × 1584 = 811,008 CMACs (using 12 subcarriers per PRB).

§6.5   Precoding in O-RAN Split 7-2x

In the O-RAN functional split 7-2x architecture, the precoding matrix W is applied by the O-DU (baseband), not the O-RU (radio head). The O-RU receives pre-processed, pre-weighted IQ samples per antenna port and performs only IFFT, cyclic prefix insertion, upconversion, and PA driving.

Beamforming Weight (BFW) Transport

BFW Volume Calculation — 32TRX, 16 Layers

BFP-9: 1 exponent byte (shared per 12-element block) + 9-bit real + 9-bit imaginary per element. Factor of ×18 = 2×9 bits per complex weight. In practice, O-RAN eCPRI headers add ~10–15 % overhead on top of IQ payload.

3GPP / O-RAN TS 38.211 §7.3.1.4 — Precoding. O-RAN.WG4.CUS.0-v13.00 §9.3 — BFW section types and compression methods.

16-Layer MU-MIMO: 4-UE Beam Directions and Layer Allocation

Bar chart showing the 16-layer split across 4 UEs (rank-4 each). UE beam groups are separated in azimuth (W₁ horizontal beam indices l₁), enabling spatial reuse. The azimuth angles correspond to the sin(φ_H) → φ mapping for a 32TRX array at d_H = λ/2.

The baseband precoding chain described here operates entirely within the O-DU. The next section details how the 32 precoded port signals are mapped to physical RF chains, how analogue beamforming is applied in hybrid architectures, and how calibration error propagates through the beamforming gain. → §7 RF Chain & Hybrid BF

§7.1 — Digital vs Analog vs Hybrid Beamforming

Every massive MIMO or beamforming deployment must choose how tightly digital signal processing couples to the antenna aperture. Three architectures dominate 3GPP deployments, each representing a different trade-off between beam-shaping precision, hardware cost, and power consumption. Understanding when each applies is essential for system design at sub-6 GHz and mmWave frequencies.

In practice, 3GPP 5G NR deployments are predominantly full digital for sub-6 GHz macro base stations (32TRX or 64TRX Active Antenna Units, AAUs), where element count is manageable and silicon cost per chain is acceptable at current process nodes. For mmWave (FR2), the large number of antenna elements needed for aperture (typically 128–512) forces hybrid or analog architectures to keep power and cost tractable. 3GPP TS 38.104 and TR 38.803 define the RF requirements within which each implementation choice must operate.

§7.2 — 3GPP 32TRX RF Chain Architecture (n78, 3.5 GHz)

The canonical sub-6 GHz massive MIMO deployment in Release 15/16 is the 32TRX Active Antenna Unit operating in band n78 (3300–3800 MHz). Each of the 32 transceiver chains is fully independent, giving complete digital beamforming capability. Understanding the RF chain architecture is prerequisite to interpreting power, EIRP, and calibration specifications.

TX RF Chain Per Port

For each of the 32 TX ports, the signal path from baseband to antenna is:

• PA per chain: typical P_max = 26 dBm (400 mW) per port for macro BS. Some deployments use 29 dBm (800 mW) GaN PAs for maximum coverage class.
• Total conducted power (max, all ports simultaneous): 32 × 26 dBm = 32 × 0.4 W = 12.8 W conducted (unrestricted). In practice total EIRP is the binding constraint, not conducted power sum.
• Amplitude + phase control: Each chain applies a complex precoder coefficient W_p (amplitude scaling + phase rotation) computed in baseband — this is the digital beamforming step. There are no analog phase shifters in this architecture.
• LO sharing: In most AAU implementations all 32 chains share a single TCXO/PLL LO reference, ensuring phase coherence to within the calibration residual (<2° after calibration).

§7.3 — PA Characteristics & Efficiency

The Power Amplifier is the dominant power consumer in any active antenna system, and its efficiency directly determines the total system power consumption. For 5G NR OFDM with high PAPR, PA design is a central engineering challenge.

PA Operating Parameters (GaN at 3.5 GHz)

• PA output power P_out: For macro BS, 26–29 dBm per port is typical. Sub-6 GHz GaN HEMT devices achieve saturation power P_sat of +33–36 dBm per device; the PA circuit is operated backed off from saturation.
• PA efficiency η_PA = P_RF / P_DC: For GaN PA at 3.5 GHz at saturation: η_PA ≈ 50–65%. At 10 dB output back-off (for OFDM PAPR): η_PA drops to ≈ 8–15% (class A/AB). With Doherty PA architecture: η_PA ≈ 25–40% at back-off.

PAPR and Output Back-Off

OFDM waveforms have high Peak-to-Average Power Ratio (PAPR). For 100 MHz NR carrier (numerology μ=1, 30 kHz SCS), PAPR ≈ 10 dB at the 10^-4 CCDF level. This means the PA must be backed off from its 1-dB compression point to avoid nonlinear distortion violating ACLR requirements (3GPP TS 38.104 ACLR ≥ 45 dBc for Wide Area BS).

Total Radiated Average Power (32TRX)

With 21 dBm average per port and 32 ports transmitting simultaneously:

§7.4 — Phase Shifter Implementation (Analog / Hybrid)

In analog or hybrid beamforming architectures (primarily FR2 mmWave, but also some FR1 compact panel AAUs), phase shifters are inserted between the RF combiner/splitter network and the antenna elements to steer the beam without per-element digital control. Understanding their quantization characteristics is essential for beam accuracy and inter-beam isolation analysis.

Phase Shifter Characteristics

• Implementation technology: Typically switched PIN-diode networks or RF MEMS for discrete phase steps. Some mmWave designs use vector modulators in silicon (28 nm CMOS).
• Resolution: Typically 4–6 bits, yielding 2^N = 16 to 64 discrete phase levels over 0–360°.
• Phase step size: Δφ = 360° / 2^N. For 4-bit: Δφ = 22.5°. For 6-bit: Δφ = 5.625°.

Phase Quantization Error and Gain Loss

When the ideal phase φ_ideal is rounded to the nearest quantized level, a residual error ε uniformly distributed in [−Δφ/2, +Δφ/2] is introduced. Its rms value is:

§7.5 — Temperature & Calibration

In a real 32TRX antenna array, phase and amplitude mismatches between RF chains are inevitable. These mismatches arise from component tolerances, PCB trace length differences, and — critically — from time-varying temperature gradients across the antenna panel. Beamforming precision degrades continuously as the system drifts from its calibration state.

Calibration Architecture

Active Antenna Units use internal calibration networks: a dedicated calibration coupler taps a small fraction of each chain's signal into a common calibration receiver (or couples a calibration tone from a central source to all chains). By measuring the complex response of each chain in the frequency domain, the DSP can compute and apply amplitude/phase correction coefficients.

• Calibration interval: Typically every 1–10 seconds for sub-6 GHz AAUs. Temperature drift rate ≈ 0.01°C/s during normal operation; component phase sensitivity ≈ 0.01–0.05 °/°C for typical CMOS LNA/mixer chains. This gives ≈ 0.001–0.005° phase drift per second per chain — manageable with 1–10 s calibration intervals.
• Calibration accuracy (post-cal residual): Typically <2° rms phase error and <0.3 dB amplitude error per chain after calibration. This is achievable with a 12-bit calibration receiver.
• Uncalibrated error: 5–10° phase error per chain (after 30–60 s without calibration) → 1–3 dB gain loss (coherent combining degrades), beam pointing error 0.5–2° (proportional to inter-element phase gradient error).
• Amplitude calibration: PA gain varies with temperature (+0.01 to +0.05 dB/°C), so the calibration must capture amplitude as well as phase. Uncalibrated amplitude imbalance of 0.5 dB across 32 chains causes <0.3 dB array gain loss (less sensitive than phase).

§7.6 — TX Signal Chain Block Diagram

The complete transmit signal chain from channel-coded bits to antenna port, including the DPD feedback loop, is described below. This represents a single port (1 of 32) in a 32TRX full-digital AAU.

Coded bits
    │
    ▼
┌──────────────────────┐
│  QAM Modulator       │  (QPSK / 16QAM / 64QAM / 256QAM)
└──────────────────────┘
    │
    ▼
┌──────────────────────┐
│  Layer Mapper        │  (for multi-layer: maps symbols to layers 1..v)
└──────────────────────┘
    │
    ▼
┌──────────────────────┐
│  Precoder W (×)      │  ← Digital BF: apply W_p ∈ ℂ per layer per port
│  (baseband, 32×v)    │    W computed from PMI / codebook / eigenbeam
└──────────────────────┘
    │
    ▼
┌──────────────────────┐
│  IFFT + CP Insert    │  (N-pt IFFT, 2048/4096 for 30 kHz SCS at 100 MHz)
│  → time-domain OFDM  │
└──────────────────────┘
    │
    ▼
┌──────────────────────┐
│  DAC (16-bit)        │  (digital → analog, fs = 245.76 MSps typical)
└──────────────────────┘
    │
    ▼
┌──────────────────────┐
│  I/Q Upconverter     │  (quadrature mixer: I·cos(2πf_LO·t) - Q·sin(2πf_LO·t))
│  LO: 3.5 GHz PLL     │
└──────────────────────┘
    │
    ▼
┌──────────────────────┐
│  BPF                 │  (100 MHz BW, suppresses image / harmonics)
└──────────────────────┘
    │
    ▼
┌──────────────────────┐    ┌──────────────────────┐
│  PA (GaN, 26 dBm)    │───►│ Coupler (observation) │──► ADC ──► DPD
│  with DPD pre-distort│    │ (−30 dBc tap)         │    update  ↑
└──────────────────────┘    └──────────────────────┘     └────────┘
    │                                                      (Feedback path)
    ▼
  ANT port (1 of 32)
    

The DPD feedback path is critical for meeting ACLR requirements without excessive back-off. The observation receiver digitises the coupled PA output at high bandwidth (≥200 MHz), allowing the DPD to model and invert the PA's nonlinear transfer function. Modern DPD implementations use Volterra series (polynomial) or neural network models, running on dedicated DSP fabric within the baseband unit. Convergence time is typically 5–20 ms, making DPD effective for stationary operation but requiring careful management during fast power ramp-up (e.g., beam switching events).

§8.1 — EIRP Definition and Calculation

Effective Isotropic Radiated Power (EIRP) is the single most important figure of merit for characterising the transmit capability of a beamforming base station in the far field. It accounts for both the conducted power at the antenna connector and the directivity gain of the antenna system in the direction of the beam.

Per-Port vs. Coherent Array Contributions

For a 32TRX array, two distinct contributions to EIRP must be distinguished:

• Single-port contribution: P_conducted = 21 dBm (average per port, with DPD) + G_element = 8 dBi (typical patch element at 3.5 GHz) = 29 dBm EIRP per port, if acting alone.
• Full array coherent combining: When all 32 ports transmit with phase-aligned precoding (beamforming towards one UE), the array factor provides an additional gain of: $$G_\text{array,dB} = 10 \cdot \log_{10}(N_\text{TRX}) = 10 \cdot \log_{10}(32) = 15\,\text{dB}$$ Total array gain: G_total = G_element + G_array = 8 + 15 = 23 dBi
  Full-array EIRP: 21 dBm + 23 dBi = 44 dBm EIRP

§8.2 — 3GPP EIRP Requirements (TS 38.104)

3GPP TS 38.104 defines BS classes with specific conducted power and EIRP limits. The table below summarises the key requirements for band n78 (3.5 GHz), which is the primary 5G NR mid-band globally.

The distinction between conducted and EIRP limits reflects the dual nature of base station regulation: conducted limits protect adjacent channel users and constrain PA non-linearity, while EIRP limits protect against excessive RF exposure and interference to other radio services. Active antenna systems must satisfy both simultaneously.

§8.3 — Free Space Path Loss & Received Power

The path loss model chosen for link budget analysis critically determines the predicted coverage and capacity. We consider both the ideal Free Space Path Loss (FSPL) and the more realistic 3GPP TR 38.901 Urban Macro (UMa) NLOS model.

Free Space Path Loss

3GPP TR 38.901 UMa NLOS Path Loss

For urban macro-cell deployments, FSPL is highly optimistic. The 3GPP TR 38.901 Table 7.4.1-1 UMa NLOS B model (the simplified form used for system-level evaluations) is:

The 27 dB difference between FSPL (97.3 dB) and UMa NLOS (124.3 dB) at 500 m represents the combined effect of building diffraction, scattering, and shadowing in a dense urban environment. The UMa NLOS model includes a log-normal shadow fading standard deviation of σ_SF = 7.82 dB (TS 38.901 Table 7.4.1-1), which should be added as a link margin in system planning.

§8.4 — Received Signal Level (RSL) Calculation

With the propagation model established, we can construct a complete downlink link budget for the 32TRX macro cell scenario in UMa NLOS at 500 m.

§8.5 — UL vs DL Beamforming Gain

A common misconception is that beamforming gain applies only to the downlink. In a 5G NR TDD system, both uplink and downlink benefit from array gain, but the mechanisms differ and the power asymmetry between UE and gNB requires careful consideration.

Downlink (DL) — gNB TX Beamforming

The gNB applies precoder W (32×1 for single-layer DL) to focus transmitted energy towards the UE. The UE receives with a single omnidirectional antenna. Array gain = N_TRX = 32 = 15 dB. This directly increases the DL RSL and DL SNR at the UE.

Uplink (UL) — gNB RX Combining

The UE transmits with P_max,UE = 23–26 dBm from a single antenna. The gNB receives across all 32 ports and applies UL combining (MRC, ZF, or MMSE) to combine the 32 received signal copies coherently. The combining gain equals the number of RX ports: G_UL,combining = 10·log₁₀(32) = 15 dB, identical to the DL beamforming gain (by receive combining theory).

This is not a coincidence — it follows directly from the duality of transmit beamforming and receive combining in a reciprocal channel. The capacity-achieving receiver applies matched filtering to the 32-element received vector, which is precisely the MRC combining operation.

TDD Reciprocity and Beam Reuse

In TDD NR, the DL and UL operate on the same frequency, so the channel matrix H is reciprocal (H_UL = H_DL^T after calibration). This means:

• The optimal DL precoder W* = leading eigenvector of H^HH, computed from UL SRS (Sounding Reference Signal) measurements.
• No DL CSI-RS beam sweeping is needed for the precoder computation — the gNB learns H from UL SRS and exploits reciprocity to construct W for DL.
• This is the foundation of Type-I and Type-II codebook precoding in 3GPP Release 15/16: the codebook entries correspond to quantized versions of the channel-matched beamforming vectors estimated from SRS.

§8.6 — Link Budget Waterfall: 1 TRX vs 32 TRX

The waterfall chart below visualises the cumulative link budget for the 32TRX beamforming scenario (d = 500 m, UMa NLOS, f = 3.5 GHz), compared to a 1 TRX (no beamforming) reference. Each bar represents one link budget component; the running total is the signal level at that stage of the chain.

The chart makes the beamforming advantage visually clear: the only difference between the two columns is the "TX Array Gain" bar (+15 dB present in the 32TRX case, absent in 1 TRX). All other elements are identical. This +15 dB propagates directly to RSL, since path loss and UE gain are fixed by the channel and UE hardware respectively. The dashed orange line marks the approximate thermal noise floor for a 100 MHz NR receiver (kTB + 7 dB NF = −174 + 80 + 7 = −87 dBm — at 100 MHz bandwidth), providing a reference for the receiver SNR at each configuration.

§8.7 — Beamforming Gain: Path Loss & Throughput Scenarios

The two charts below place beamforming gain in a practical systems context: first showing how array gain extends usable coverage range across MCS thresholds, then showing the compounding effect of MU-MIMO spatial multiplexing on total cell throughput.

Chart A — RSL vs Distance: Omni vs 8TRX vs 32TRX vs 64TRX

UMa NLOS path loss at 3.5 GHz: PL(d) = 13.54 + 39.08·log₁₀(d) + 20·log₁₀(3.5) = 24.42 + 39.08·log₁₀(d) dB. RSL(d) = EIRP − PL(d). Horizontal lines show the minimum RSL required to sustain each MCS tier (noise floor = −87 dBm; required SINR added per MCS).

Each RSL curve's intersection with an MCS threshold line marks the maximum distance at which that MCS is sustainable. 32TRX extends MCS-28 range from ~95 m (1TRX) to ~265 m; 64TRX pushes it to ~340 m. Coverage-limit range (noise floor) increases from ~250 m (1TRX) to ~760 m (64TRX).

Chart B — Throughput Comparison at 500 m (SU vs MU-MIMO)

At 500 m UMa NLOS, different antenna configurations achieve very different SINR levels. TP = layers × N_RB × 12 × N_sym × R × log₂(M) / T_slot, with N_RB=132, N_sym=12 (14−2 DMRS), T_slot=0.5 ms. MU-MIMO reduces per-UE SINR by ~3–5 dB due to residual inter-user interference, but multiplexes more independent streams simultaneously.

MU-MIMO scenarios (D, E) achieve higher sum throughput by serving multiple UEs simultaneously on orthogonal spatial streams. The per-UE rate is lower, but the total cell capacity more than doubles vs 32TRX SU-MIMO (Scenario C). Parameters: 100 MHz NR, n78, FR1, 30 kHz SCS, 132 RB, slot format 5/9 (12 data symbols).

§11.1 — 3D Beamforming Overview

Legacy 2D beamforming systems operate exclusively in the horizontal (azimuth) plane. A linear array of antenna elements shapes the beam left and right, but the vertical radiation pattern is fixed — set once at installation via mechanical tilt of the antenna panel. This imposes a fundamental constraint: all user equipment (UE) within a sector, whether on a ground floor or the top of a high-rise building, is served with the same elevation beam. The resulting signal mismatch degrades both coverage and capacity for vertically distributed populations.

Full-Dimension MIMO (FD-MIMO) — standardised in 3GPP TR 36.897 for LTE and extended into 5G NR in TS 38.214 §5.2.2 — resolves this limitation by deploying a two-dimensional Uniform Planar Array (UPA). The UPA has both horizontal (N_H) and vertical (N_V) elements, enabling independent beam control in both azimuth and elevation. The resulting 3D beam can be steered in two orthogonal planes simultaneously, a capability described in the literature as Full-Dimension MIMO or 3D beamforming.

For a 32TRX system with the canonical 8×4×2 physical configuration (N_H = 8 horizontal dual-polarised columns, N_V = 4 vertical rows, 2 polarisations per element), the resulting UPA controls:

• Azimuth beam: shaped by the 8-column horizontal aperture → HPBW ≈ 14.4° at λ/2 element spacing (d_H = 0.5λ)
• Elevation beam: shaped by the 4-row vertical aperture → VPBW ≈ 25.4° at λ/2 element spacing (d_V = 0.5λ)
• Polarisation diversity: each of the 32 logical ports corresponds to one polarisation of one sub-array, enabling cross-polarisation MIMO streams

[1] 3GPP TR 36.897 v13.0.0 — Study on elevation beamforming / Full-Dimension MIMO for LTE. 3rd Generation Partnership Project, 2015.

[2] 3GPP TS 38.214 v17.4.0 — NR: Physical layer procedures for data, §5.2.2 (Codebook-based precoding for PDSCH). 3GPP RAN1, 2023.

§11.2 — Elevation Beamforming for 32TRX (N_V = 4)

The 3GPP channel model standard TR 38.901 defines the zenith angle of departure (ZoD) — measured from the vertical axis (broadside = 90°). For a typical urban macro (UMa) scenario, the mean ZoD at the base station is approximately 100° (10° below the horizon), reflecting the geometry of a tower antenna illuminating street-level UEs.

Elevation Beamwidth Formula

For a uniform linear array with N_V elements at spacing d_V = λ/2, the half-power beamwidth (HPBW) in the elevation plane is:

For the 32TRX configuration with N_V = 4:

This means adjacent elevation beams spaced by 25.4° can be fully resolved without significant inter-beam interference. The grating-lobe-free scan range is bounded by:

In practice, element pattern roll-off limits the useful scan range to approximately ±25° elevation from boresight for a 4-row array.

High-Rise Building Coverage Analysis

Consider a 20-story building at 200 m horizontal distance from the base station (25 m tower height). Each story is approximately 3 m, giving a building height span from ground (0 m) to rooftop (60 m above ground level). The subtended elevation angle span at the base station is:

With BW_V = 25.4° for N_V = 4, the number of independently resolvable elevation beam positions covering this 16.7° span is:

This is sufficient to separate rooftop UEs from ground-floor UEs, but provides no further granularity across intermediate floors. Increasing to N_V = 8 doubles the resolution:

With N_V = 8 (64TRX), 4 independent floor groups can be served simultaneously — enabling lower, mid, upper-mid, and rooftop zones to receive distinct elevation beams, substantially reducing inter-floor co-channel interference in high-rise dense urban deployments.

§11.3 — Electrical Tilt Control

Two mechanisms are available to adjust the vertical pointing of a cellular antenna: mechanical tilt and electrical tilt (ET). In 5G NR FD-MIMO, both are used in combination.

Mechanical vs. Electrical Tilt

Mechanical tilt involves physically rotating the antenna panel downward from the horizontal plane. This is set once at installation (typically 3–10° for macro base stations) and cannot be changed without a site visit. Mechanical tilt shifts the entire radiation pattern — both the main lobe and sidelobes — providing coarse coverage shaping.

Electrical tilt is achieved via baseband signal processing: a linear phase progression is applied across the vertical elements of the array. For an N_V-element vertical array with inter-element spacing d_V, the phase applied to element index \(v = 0, 1, \ldots, N_V - 1\) to steer the beam to elevation angle \(\theta_{ET}\) relative to broadside is:

where \(\theta_{ET}\) is measured from the horizontal plane (positive = upward tilt, negative = downward tilt). For d_V = λ/2:

The combined pointing angle of the radiated beam is:

For a 32TRX panel (N_V = 4) with d_V = λ/2, the practical electrical tilt range before grating lobe emergence is approximately ±15°. This gives an effective total tilt range of:

• Minimum downward tilt: θ_mech + 15° (e.g., 6° + 15° = 21° total downtilt for UDN)
• Maximum upward tilt: θ_mech − 15° (e.g., 6° − 15° = −9° → pointing above horizon — used for HAPS or elevated relay scenarios)

[3] 3GPP TR 38.901 v17.0.0 — Study on channel model for frequencies from 0.5 to 100 GHz, §7.3 (Antenna modelling), §7.5 (UMa ZoD statistics). 3GPP RAN1, 2022.

§11.4 — 3D Beamsteering Coverage Map (System Design)

For a 32TRX macro base station at 25 m height with 200 m inter-site distance (ISD) in a three-sector deployment, the 3D beam grid is defined as follows:

SSB Beam Configuration vs L_max

The SSB (Synchronisation Signal Block) beam sweep governs how many distinct elevation and azimuth beams the gNB transmits during the initial access procedure. The maximum SSB beam count L_max is frequency-range dependent:

For a 32TRX n78 (3.5 GHz) deployment with L_max = 8, the operator can choose between an 8-beam azimuth-only sweep (ignoring elevation diversity in SSB) or a 4-azimuth × 2-elevation configuration that covers both high-rise and street-level UEs during the initial beam sweep. The latter is increasingly common in 5G SA deployments in Asia-Pacific high-rise markets (South Korea, Japan, mainland China).

§11.5 — Beamforming Gain vs. Tilt Angle (Scan Loss)

As a phased-array beam steers away from boresight, the projected aperture of the array diminishes. This causes a reduction in array gain known as scan loss, which must be accounted for in the link budget at cell edge.

Horizontal Scan Loss

For an N_H-element horizontal array with isotropic elements, the array factor magnitude in the scan direction is proportional to \(\sin(N_H \psi / 2) / \sin(\psi / 2)\) where \(\psi = 2\pi d_H (\sin\phi - \sin\phi_0)/\lambda\). Near broadside, this simplifies to an effective aperture reduction:

At the sector edge (\(\phi = 60°\) from boresight):

Vertical Scan Loss

With only N_V = 4 vertical elements, the elevation aperture is modest and the corresponding scan loss is smaller:

Combined Scan Loss at Cell Edge

For a UE at azimuth φ = 60° (sector edge) and elevation θ = −5° below horizon (street-level at 200 m):

This 6.5 dB scan loss from peak EIRP must be added as a margin in the cell-edge link budget. In practice, operators dimension coverage at the beam boresight and accept the scan-loss degradation at cell edges as a boundary condition, relying on inter-cell handover to keep UEs on beams within ±30° of boresight for nominal operation.

§11.6 — Deployment Configurations

The heatmap above illustrates the 3D beam pattern of the 32TRX array steered to the nominal UMa boresight direction (φ = 0°, θ = −2° below horizon). The main lobe peak (44 dBm average EIRP) is surrounded by sidelobe structures both in azimuth (spaced at ~14.4°, the HPBW of the 8-element horizontal sub-array) and in elevation (spaced at ~25.4°, the VPBW of the 4-element vertical sub-array). The dotted lines indicate the −3 dB beamwidth boundaries in each dimension.

[4] 3GPP TS 38.214 v17.4.0 §5.2.2.2 — Type II CSI codebook, elevation oversampling factors O_1, O_2. 3GPP RAN1, 2023.

[5] 3GPP TR 36.897 v13.0.0 §5 — Elevation beamforming antenna modelling and UPA configuration for FD-MIMO. 3GPP RAN1, 2015.

11.7 — Beam Pattern Scenarios: SU, MU-MIMO, Cell Edge

Three canonical beamforming scenarios computed for the 32TRX (N_H=8) array at 3.5 GHz. All patterns derived from the UPA array factor; MU-MIMO patterns include ZF null constraints.

§12.1 — Full System Link Budget (32TRX, 100 MHz, n78, UMa NLOS)

A link budget is a systematic accounting of every gain and loss in the signal path from transmitter power amplifier output to the receiver's noise floor. For a 5G NR downlink with 32TRX beamforming, the budget quantifies the maximum allowable path loss and, from that, the maximum cell range for each modulation and coding scheme (MCS).

The scenario below uses: 3.5 GHz (band n78), 100 MHz carrier bandwidth, 32TRX macro base station, UMa NLOS path loss model from TR 38.901, single UE with omnidirectional receive antenna.

Downlink Link Budget — Parameter Table

§12.2 — Range Extension Due to Beamforming

The relationship between path loss budget and maximum range follows the TR 38.901 UMa NLOS path loss equation. Let PL_max denote the maximum tolerable path loss:

The TR 38.901 UMa NLOS model at 3.5 GHz is:

Without Beamforming (1TRX)

EIRP = 26 − 0.5 − 5 + 8 + 0 = 28.5 dBm:

With 1TRX, MCS 0 coverage extends only to approximately 144 m — insufficient for a 200–500 m ISD macro deployment.

With 32TRX Beamforming

EIRP = 43.55 dBm:

Maximum Range for Higher MCS

For MCS 16 (64QAM, R = 0.48, required SINR ≈ +14.1 dB) with 32TRX:

MCS 16 (64QAM) is achievable only within approximately 118 m of the 32TRX macro station under UMa NLOS conditions at 90% coverage probability — consistent with typical operator experience that 64QAM is dominant only in the inner third of the cell radius.

Note that the range gain ratio is constant at 3.17× across all MCS levels — this is a mathematical consequence of the path loss exponent (30 = 3.0 in this model) and the fixed beamforming gain (15 dB):

where α = 3.0 is the path loss exponent for UMa NLOS in TR 38.901 (the 30·log₁₀(d) term corresponds to α = 3).

§12.3 — Throughput Calculation

The 5G NR PDSCH throughput (TS 38.214 §5.1.3.2) follows the general formula adapted from the NR downlink peak rate expression:

where:

• \(\nu\): number of MIMO layers (spatial streams) — up to 8 per UE in 5G NR DL
• \(Q_m\): modulation order (2=QPSK, 4=16QAM, 6=64QAM, 8=256QAM)
• \(R_c\): target code rate (fraction)
• \(N_{\rm PRB}^{\rm BW,\mu}\): number of PRBs for bandwidth BW at SCS μ; for 100 MHz, SCS 30 kHz (μ=1): N_PRB = 132 PRBs
• \(N_{\rm DMRS}\): demodulation reference signal overhead — typically 2 OFDM symbols per slot for single-DMRS port (reduced to 1 for front-loaded in some configs)
• \(N_{\rm OH}\): overhead symbols (PDCCH, CSI-RS, SSB within the slot): typically 1–2 symbols per slot
• \(T_s^\mu\): slot duration = 0.5 ms for μ=1 (30 kHz SCS)

Peak Throughput Estimate: 32TRX, 16-layer SU-MIMO, MCS 28

Configuration: 16 spatial layers (requires two co-located 32TRX panels or advanced 8-layer per UE with FDD MU-MIMO pairing), MCS 28 (256QAM, R_c = 0.926), 100 MHz bandwidth (132 PRBs), SCS 30 kHz:

Accounting for practical overheads (PDCCH occupancy ~1 symbol, CSI-RS ~1 symbol/slot, SSB on average 0.5 symbols/slot, TDD DL:UL ratio 7:2 + 1 special = 10 slots, effective DL ratio = 70%):

This approximately 3.0 Gbps peak DL throughput is consistent with reported field measurements from commercial 32TRX deployments in n78 100 MHz configurations (e.g., T-Mobile US, NTT Docomo Japan — field trials have reported 2.8–3.5 Gbps peak single-cell DL under ideal conditions with carrier aggregation or 2×100 MHz NR-CA).

§12.4 — Beamforming Gain Summary

The beamforming gain figures above are derived from the following scaling laws, with all comparisons made at equal total radiated power:

where α = 3.0 for UMa NLOS, giving range gain = 10^(log₁₀(N)/3) = N^(1/3):

• 8TRX: 8^(1/3) = 2.0× range
• 32TRX: 32^(1/3) = 3.17× range
• 64TRX: 64^(1/3) = 4.0× range

The chart illustrates the dramatic range advantage of massive antenna arrays. The 64TRX configuration (red) maintains useful throughput at nearly twice the distance of 8TRX (blue), while 32TRX (green) represents the practical commercial sweet-spot — sufficient range for 200–500 m ISD deployment with meaningful MCS-diversity at all distances within the cell. The dotted reference lines at 200 m and 500 m mark typical urban macro ISD boundaries.

[6] 3GPP TR 38.901 v17.0.0 §7.4.1 — UMa path loss model (LOS and NLOS). 3GPP RAN1, 2022.

[7] 3GPP TS 38.214 v17.4.0 §5.1.3.2 — MCS tables for PDSCH, 256QAM, code rate mapping. 3GPP RAN1, 2023.

[8] 3GPP TS 38.101-1 v17.6.0 §7.3.1 — UE noise figure requirements for FR1. 3GPP RAN4, 2023.

[9] 3GPP TS 38.331 v17.4.0 §6.3.2 — CSI-RS resource configuration and beam management framework. 3GPP RAN2, 2023.

§13.1 — CSI-RS for Beam Management (TS 38.211 §7.4.1.5)

Channel State Information Reference Signals (CSI-RS) are pilot sequences transmitted by the gNB that allow the UE to measure channel quality, estimate the precoding matrix, and report beam-quality metrics back to the network. While CSI-RS has multiple applications (channel estimation for CSI feedback, RSRP measurement, mobility, RRM), its role in Beam Management (BM) is of central importance in massive MIMO systems.

For beam management, the gNB transmits a set of beamformed CSI-RS resources, one per candidate beam. Each resource carries an independent precoding vector \(\mathbf{w}_b \in \mathbb{C}^{N_T \times 1}\), so that the UE receives the spatial signature of each candidate beam during a single measurement occasion. The UE measures the L1-RSRP (Layer-1 Reference Signal Received Power) for each CSI-RS resource and reports the best beam via a CRI (CSI-RS Resource Indicator) in the CSI report.

Beam Sweeping with N_beams Candidate Beams

For a system with \(N_{\rm beams}\) candidate beams, the gNB schedules \(N_{\rm beams}\) CSI-RS resources, each with precoder \(\mathbf{w}_b\), \(b = 1, \ldots, N_{\rm beams}\). The received signal at the UE on beam \(b\) is:

where \(\mathbf{h} \in \mathbb{C}^{N_T \times 1}\) is the DL channel vector, \(s\) is the reference signal (known to UE), and \(n \sim \mathcal{CN}(0, \sigma_n^2)\) is noise. The UE computes L1-RSRP for each beam:

The UE reports the index \(b^* = \arg\max_b \,\text{RSRP}_b\) as the CRI. The gNB then uses \(\mathbf{w}_{b^*}\) as the serving beam precoder for subsequent PDSCH transmissions.

P3 Procedure — Periodic L1-RSRP Reporting

The P3 procedure (TS 38.214 §5.2.1.3) performs beam tracking: the UE periodically measures L1-RSRP on the current serving beam's CSI-RS resource without re-sweeping the full beam set. This keeps overhead low during steady-state operation. If the RSRP of the serving beam drops more than the hysteresis threshold (\(\Delta_{\rm hys} = 3\) dB), the UE triggers a P1/P2 re-selection event.

[1] 3GPP TS 38.211 v17.4.0 §7.4.1.5 — CSI reference signals. 3GPP RAN1, 2023.

[2] 3GPP TS 38.214 v17.4.0 §5.2.1.3 — UE procedure for reporting L1-RSRP. 3GPP RAN1, 2023.

§13.2 — SSB Beam Sweeping (TS 38.211 §7.4.2–7.4.3)

The SS/PBCH Block (SSB) is the fundamental broadcast signal of 5G NR. Each SSB carries:

• PSS (Primary Synchronisation Signal) — for frequency/timing acquisition
• SSS (Secondary Synchronisation Signal) — for cell ID detection
• PBCH (Physical Broadcast Channel) — carries the MIB and SSB beam index

An SSB occupies 4 OFDM symbols × 20 PRBs (240 subcarriers), and multiple SSBs are grouped into an SS burst set transmitted once every 20 ms half-frame period. The gNB transmits each SSB with a different analog beam, performing a spatial sweep so that every UE — regardless of direction — can detect at least one SSB.

L_max and FR1/FR2 Rules

For n78 (3.5 GHz, μ=1) — the dominant 5G NR mid-band: \(L_{\max} = 8\). Within the 5 ms half-frame, 8 SSBs are placed at pre-defined OFDM symbol positions (symbols 2, 8 in slots 0–3 of the half-frame). Each SSB carries a beam index encoded in the 3 LSBs of the PBCH payload; the UE identifies its serving SSB (and therefore the gNB's beam direction) without any uplink signalling.

Angular Resolution: SSB vs. CSI-RS Beams

The angular coverage per SSB beam for a sector-wide sweep of ±60° (total 120°):

Contrast this with the CSI-RS beam resolution for a Type I Single-Panel codebook (O_1 = 4 oversampling, N_1 = 4 horizontal ports):

[3] 3GPP TS 38.211 v17.4.0 §7.4.2–7.4.3 — SS/PBCH block structure and timing. 3GPP RAN1, 2023.

[4] 3GPP TS 38.213 v17.4.0 §4.1 — Cell search and SSB timing. 3GPP RAN1, 2023.

§13.3 — Beam Management Procedures P1, P2, P3 (TS 38.214 §5.2.1.2)

3GPP defines three hierarchical beam management procedures, each operating at progressively finer spatial granularity:

BM State Machine

The beam management process operates as a state machine. On initial access, the system enters the P1 state. After beam group selection, it advances to P2 for refinement, then transitions to P3 for steady-state tracking. Degradation events drive transitions back toward P1:

[5] 3GPP TS 38.214 v17.4.0 §5.2.1.2 — CSI-RS for beam management (P1/P2/P3 procedures). 3GPP RAN1, 2023.

§13.4 — SRS for Uplink Beam Management (TS 38.211 §6.4.1.4)

The Sounding Reference Signal (SRS) serves the uplink counterpart of CSI-RS. The UE transmits SRS sequences across the bandwidth; the gNB processes received SRS to estimate the UL channel for:

• UL beam selection (for UL MIMO / PUSCH beamforming)
• DL beamforming via TDD reciprocity (channel reciprocity enables the gNB to compute DL beamforming weights directly from UL SRS estimates, eliminating DL CSI feedback)
• Full-band channel sounding (frequency hopping across all 132 PRBs in 100 MHz)

TDD Reciprocity Path

With TDD operation (DL and UL use the same frequency), the channel is reciprocal (in the absence of Rx/Tx calibration errors):

The gNB forms the DL beamforming weight by processing the received SRS:

where \(\mathbf{S}\) is the known SRS sequence matrix and \(\mathbf{u}\) is the layer selection vector. This reciprocity-based beamforming is how commercial 32TRX massive MIMO systems (e.g., commercial 32TRX products) compute their DL beams in practice — from UL SRS rather than DL PMI feedback.

SRS Resource Configuration

SRS is configured via RRC (SRS-Resource, SRS-ResourceSet). Key parameters:

For a DDDSUUDDDD TDD pattern (10-slot period, slots 4–5 are UL), SRS is placed in slot 4 or 5. With 128 simultaneous UEs, each transmitting 1 SRS port, the gNB must process 128 SRS sequences per 10 ms SRS period — fully occupying the UL processing pipeline of the baseband unit during SRS slots.

[6] 3GPP TS 38.211 v17.4.0 §6.4.1.4 — Sounding reference signals. 3GPP RAN1, 2023.

[7] 3GPP TS 38.214 v17.4.0 §6.1.1 — UE procedure for SRS transmission. 3GPP RAN1, 2023.

§13.5 — CSI-RS Port Configuration for 32TRX (TS 38.211 Table 7.4.1.5.3-1)

A 32TRX AAS requires 32 orthogonal CSI-RS ports to fully sound the DL channel across all antenna elements. 3GPP TS 38.211 §7.4.1.5 defines four CDM (Code-Division Multiplexing) types that multiplex multiple ports onto shared time–frequency resources. The choice of CDM type determines the number of OFDM symbols and subcarrier pairs consumed per CSI-RS occasion.

For the dominant 32-port configuration in commercial deployments: two 16-port FD-CDM2 resources are stacked across 2 OFDM symbols, yielding 32 orthogonal CSI-RS ports in only 2 OFDM symbols. The RE overhead is:

For a periodic CSI-RS with 10 ms periodicity over 132 PRBs:

This low overhead (under 0.5%) makes dense CSI-RS configurations practical even for 32TRX systems with full-bandwidth sounding.

[8] 3GPP TS 38.211 v17.4.0 §7.4.1.5 + Table 7.4.1.5.3-1 — CSI reference signals, port mapping and CDM types. 3GPP RAN1, 2023.

§13.6 — Beam Failure Detection & Recovery (BFR)

In 5G NR, a beam failure occurs when the serving beam's quality degrades to the point where the UE can no longer reliably decode PDCCH. This can arise from sudden blockage (human body, moving vehicle), rapid UE rotation, or beam mis-alignment due to poor tracking. The BFR procedure allows the UE to autonomously recover without a full RRC re-establishment.

Beam Failure Detection (BFD)

The UE monitors a set of configured reference signals (BFD-RS: SSB or CSI-RS). A beam failure is declared when both conditions hold for \(N_{\rm BFD}\) consecutive monitoring instances:

where \(\theta_{\rm BFD}\) is the configured beam failure detection threshold (typically \(-\)110 to \(-\)130 dBm) and the 10% BLER criterion is evaluated by the UE using a hypothetical PDCCH performance model. \(N_{\rm BFD}\) is configured by RRC (beamFailureDetectionTimer: 1–16 half-frames).

Candidate Beam Identification & Recovery

Concurrently with BFD monitoring, the UE evaluates a candidate beam set (CBS): a list of alternative SSB or CSI-RS resources with quality above a recovery threshold \(\theta_{\rm CBR}\). When beam failure is declared and a candidate beam with RSRP > \(\theta_{\rm CBR}\) is available, the UE initiates recovery:

1. BFR-PRACH: UE transmits PRACH on the PRACH occasion associated with the candidate beam (the association between PRACH occasions and SSB indices is defined by TS 38.213 §8.1). This is a contention-free PRACH using a dedicated preamble.
2. BFR-MAC CE: After receiving the RA response on the candidate beam, the UE sends a Beam Failure Recovery Request via MAC CE in UL, identifying the failed beam and the new serving beam.
3. gNB Response: The gNB responds with a TC-RNTI on the candidate beam's PDCCH, activating the new serving beam. The entire BFR latency target is <10 ms (1–2 PRACH opportunities at 5 ms period).

[9] 3GPP TS 38.321 v17.4.0 §5.17 — MAC-layer beam failure recovery. 3GPP RAN2, 2023.

[10] 3GPP TS 38.331 v17.4.0 §5.3.7 — RRC beam failure recovery. 3GPP RAN2, 2023.

[11] 3GPP TS 38.213 v17.4.0 §8.1 — PRACH occasion to SSB index mapping for BFR. 3GPP RAN1, 2023.

The timeline above shows two complete DDDSUUDDDD periods (10 ms). P1 SSB beam sweeping occurs at the start of each period (DL slot 0) to maintain beam group awareness. P2 CSI-RS refinement is triggered in DL slot 2 after the CRI from P1 is received. P3 tracking CSI-RS is collocated with periodic SSB slots. SRS occupies the two UL slots (4, 5 in a 0-indexed 10-slot period). The dotted vertical line marks the period boundary; the simulated RSRP drop in period 2 (slot 11) triggers a P1 re-entry event.

§13.7 — Beam Sweep Animation & Channel Visualization

Chart A — gNB Beam Sweep Sequence (SSB P1 Procedure)

Chart B — Beam Tracking: Moving UE (−30° → +30°, 2 s)

Chart C — Cluster Channel Matrix |H|: 32 TX Ports × 4 UE RX Antennas

§14.1 — O-RAN Split 7-2x and Beamforming Responsibility

The O-RAN Alliance defines a set of functional splits that partition the 5G NR protocol stack between a centralised unit (O-DU, Open Distributed Unit) and a remote radio unit (O-RU, Open Radio Unit). The dominant split for massive MIMO deployments is Split 7-2x, which draws the boundary at the IFFT:

• O-DU side: PDCP, RLC, MAC, HARQ, resource mapping, digital precoding (W), layer mapping, RE mapping — all PHY-HIGH functions including beamforming weight computation.
• O-RU side: per-antenna iFFT, cyclic prefix (CP) insertion, DAC, RF up-conversion, power amplification, and antenna radiation — all PHY-LOW functions treating each antenna as an independent IQ stream.

Beamforming Weights (BFW) are the complex precoding coefficients that define how the O-DU's layer IQ samples are combined across O-RU antenna ports. The data flow is:

[12] O-RAN.WG4.CUS.0-v08.00 §4.3.2 — Functional split and O-RU beamforming responsibilities. O-RAN Alliance, 2023.

§14.2 — BFW Data Volume Analysis

The BFW volume is the product of the number of antenna ports, subcarriers (PRBs), and layers. For a 32TRX 100 MHz system with \(N_L = 16\) layers:

The 4.32 Gbps BFW overhead alone exceeds one quarter of a 25GbE fronthaul link, without even counting the IQ data streams. Two complementary techniques are mandated in O-RAN deployments to bring this to acceptable levels: BFW compression and BFW granularity reduction.

§14.3 — BFW Compression: BFP (Block Floating Point)

Block Floating Point (BFP) is the primary compression method specified in O-RAN.WG4.CUS for both IQ data and BFW. In BFP, a block of \(N_{\rm samp}\) real samples (e.g., one PRB's I-samples or Q-samples) share a single exponent, with each sample stored as a fixed mantissa.

BFP-9 Format

The most widely deployed BFW compression is BFP-9: 9-bit mantissa per I and Q sample, plus one 4-bit block exponent shared across all samples in a PRB (12 subcarriers):

BFW Volume After Compression

Still 2.47 Gbps for BFW alone. The second lever is subband / wideband granularity reduction. In wideband BFW mode, a single weight is used per port per layer across the entire bandwidth (no per-PRB variation):

[13] O-RAN.WG4.CUS.0-v08.00 §5.4.3 — BFW compression and BFP format. O-RAN Alliance, 2023.

§14.4 — eAxC ID Structure for 32TRX

An eAxC (extended Antenna Carrier) is the fundamental logical stream unit in the O-RAN C/U-plane. Each eAxC carries the IQ samples for a single antenna port on a single carrier — one independent IQ data stream flowing from O-DU to O-RU (DL) or O-RU to O-DU (UL). The eAxC is identified by a 16-bit eAxC ID embedded in each eCPRI packet header:

For a 32TRX system with one component carrier and one sector:

• 32 DL eAxC streams: ruPortId = 0..31, ccId = 0, bandSectorId = 0
• 32 UL eAxC streams: same structure, transmitted in the opposite direction (O-RU → O-DU during UL slots)
• Total eAxC count: 64 streams (32 DL + 32 UL)

Per-eAxC Bandwidth

For 100 MHz (n78), the sampling rate after IQ compression:

[14] O-RAN.WG4.CUS.0-v08.00 §5.1 — eAxC ID structure and mapping. O-RAN Alliance, 2023.

[15] 3GPP TS 38.104 v17.6.0 Table 5.3.2-1 — NR operating band channel bandwidth and minimum guardbands (n78, 100 MHz: 132 PRBs). 3GPP RAN4, 2023.

§14.5 — Section Types for Beamforming (O-RAN.WG4.CUS §5.4)

The O-RAN C-plane (Control Plane) uses Section Types to communicate scheduling instructions from O-DU to O-RU. Each Section Type carries different metadata — including whether BFW are present and how they are applied:

For MU-MIMO operation (§10), the gNB schedules multiple UEs on the same time–frequency resource. Each UE requires its own independent BFW set to spatially separate the co-scheduled streams. Section Type 6 carries per-UE BFW, allowing the O-RU to perform the spatial superposition:

where \(u\) indexes co-scheduled UEs and \(N_L^{(u)}\) is the number of layers for UE \(u\). With 8 UEs × 2 layers each and 32 ports, the O-RU must apply \(32 \times 8 \times 2 = 512\) complex multiply-accumulates per subcarrier per Section Type 6 operation.

[16] O-RAN.WG4.CUS.0-v08.00 §5.4 — Section types and BFW extensions. O-RAN Alliance, 2023.

The stacked bar chart illustrates how the four components of fronthaul bandwidth (IQ DL, IQ UL, BFW overhead, C-plane) evolve across four compression scenarios:

• Scenario A (uncompressed): The combined DL + UL IQ budget already reaches ~252 Gbps — more than 2.5 times the 100GbE limit even before BFW is counted. Completely impractical.
• Scenario B (BFP-9 + full-band BFW): IQ drops to ~144 Gbps; BFW contribution is 2.47 Gbps (modest after compression). Still exceeds 100GbE if DL and UL are counted together.
• Scenario C (BFP-9 + subband BFW, N_sb=4): BFW drops to 0.55 Gbps. In TDD (DL or UL at any instant), the peak active rate is ~72 Gbps — within 100GbE budget, viable with some headroom.
• Scenario D (BFP-9 + wideband BFW): BFW becomes negligible (33 Mbps). Peak TDD active rate ~72 Gbps. Practical on 100GbE; can approach 25GbE with additional tricks (reduced antenna ports, lower sampling rate).

Active Antenna System (AAS) base stations with integrated antenna arrays cannot be tested by connecting a cable to a conducted RF port — the radiating elements are embedded inside the unit and there is no accessible conducted port for a traditional power meter or spectrum analyser. Over-the-Air (OTA) testing has therefore become the mandated conformance methodology for 5G NR AAS equipment, codified across TS 38.104 §9, TS 38.131, and TS 38.141-2.

§15.1 — OTA Test Concepts

Traditional conducted (cabled) testing measures signal power and quality at the antenna connector. For an AAS BS, no such connector exists: the power amplifiers, digital beamforming network, and antenna elements form a single sealed module. OTA testing instead measures radiated power and sensitivity from the far field of the antenna aperture, inside a controlled anechoic environment.

Four primary OTA metrics are defined by 3GPP for AAS conformance:

§15.2 — 3GPP AAS BS (Active Antenna System) Standards

The 3GPP standardisation of AAS OTA conformance spans three primary documents, each addressing a different scope:

Key quantitative requirements from TS 38.104 for Wide Area BS (macro cell, e.g., n78 3.5 GHz):

• Maximum EIRP: ≤ 65 dBm per carrier (TS 38.104 Table 6.3.1.2-1) — regulatory upper bound on radiated power density
• Minimum peak EIRP: ≥ 45 dBm — ensures coverage performance for the cell-edge link budget
• EIRP accuracy: ±2.5 dB across the full power control range (TS 38.104 §6.3.2) — controls DL interference to neighbours
• Beam peak direction accuracy: ±15° in both azimuth and elevation (TS 38.104 §6.3.2) — ensures the beam lands on the intended UE and not an interfered direction

§15.3 — OTA Measurement Setup

OTA measurements require an anechoic test environment that suppresses multipath reflections and provides a quiet zone with well-characterised amplitude and phase. Two main configurations are used for AAS BS conformance:

§15.3.1 Compact Antenna Test Range (CATR)

A CATR uses a large parabolic or serrated-edge reflector to collimate a point-source feed into a plane wave across a quiet zone. A 1 m quiet zone diameter is typical for macro AAS. The range length is typically 8–15 m. Key CATR environment requirements:

• Reflectivity of chamber walls: < −40 dB (anechoic absorbers, RF-damped wedges)
• Quiet zone amplitude ripple: < ±0.5 dB (spatially across the quiet zone)
• Quiet zone phase ripple: < ±3° (ensures plane-wave condition for far-field pattern validity)
• Cross-polar isolation: > 40 dB

§15.3.2 Near-Field to Far-Field (NF→FF) Transformation

An alternative to CATR is near-field scanning: a calibrated probe samples the electromagnetic field on a sphere (or plane/cylinder) at close range, and a mathematical transformation computes the equivalent far-field pattern. For an AAS BS:

• The AUT (Antenna Under Test) is mounted on a precision positioner. The probe moves in a spherical grid — or equivalently the AUT rotates — collecting amplitude and phase at each grid point.
• A full 3D spherical pattern (360° azimuth × 180° elevation) at 5° step resolution requires 2592 measurement points and typically takes 15–30 minutes.
• The NF→FF algorithm applies a spherical wave expansion (SWE) or plane wave spectrum (PWS) transformation. For 5G FR1 AAS with aperture ~0.5 m, the required minimum NF scan distance is ≈ 0.62·\(\sqrt{D^3/\lambda}\) ≈ 0.3–0.5 m.

§15.4 — Beam EIRP Measurement Procedure (TS 38.104 §9.1)

The EIRP of each configured beam is measured following a two-stage scan procedure defined in TS 38.104 §9.1:

1. Coarse beam peak search: The AUT (or probe) rotates in 5° steps across the full upper hemisphere (or declared service volume). EIRP is recorded at each grid point. The coarse peak direction (φ_peak, θ_peak) is identified as the grid point with maximum received power.
2. Fine beam peak refinement: A dense 1° step grid is measured within ±10° of the coarse peak. The final beam peak direction is taken as the maximum of this fine scan.
3. EIRP at beam peak: The EIRP is computed from the received power at the measurement probe using the Friis transmission equation:
   $$\text{EIRP} \;[\text{dBm}] \;=\; P_\text{rx}\,[\text{dBm}] \;+\; \text{FSPL}(d)\,[\text{dB}] \;-\; G_\text{rx}\,[\text{dBi}]$$
   where \(\text{FSPL}(d) = 20\log_{10}(4\pi d/\lambda)\) is the free-space path loss at the probe distance \(d\), and \(G_\text{rx}\) is the calibrated gain of the receive probe antenna.
4. Repeat for all configured beams: For a typical Wide Area BS with \(L=8\) SSB beams and up to 64 CSI-RS beams, each beam requires a full coarse + fine scan cycle. EIRP is recorded for each beam.
5. EIRP CDF test: The cumulative distribution function (CDF) of EIRP across all configured beams is computed. TS 38.104 requires the minimum EIRP ≥ 45 dBm at the 95th percentile of the CDF (i.e., at least 95% of beams must meet the minimum EIRP floor).

§15.5 — Beam Correspondence Test

TDD massive MIMO relies on channel reciprocity: the downlink channel \(\mathbf{H}_\text{DL}\) and uplink channel \(\mathbf{H}_\text{UL}\) are related by transposition (ignoring RF impairments). If the DL beam is steered to peak at direction (φ, θ), the UL beam formed on the same set of ports should also be maximally sensitive in direction (φ, θ). This is beam correspondence.

The beam correspondence test verifies this reciprocity in the OTA environment:

1. Measure the DL EIRP beam peak direction (φ_DL, θ_DL) using the procedure in §15.4.
2. Configure the UL receive beam corresponding to the same beam index.
3. Measure the UL EIS (Effective Isotropic Sensitivity) as a function of angle in the neighbourhood of (φ_DL, θ_DL).
4. Verify that the EIS minimum (best sensitivity) occurs at (φ_UL, θ_UL) and that the angular separation \(\Delta\theta = \arccos(\hat{\mathbf{u}}_\text{DL}\cdot\hat{\mathbf{u}}_\text{UL})\) satisfies:

This 15° tolerance is identical to the beam peak direction accuracy requirement, ensuring that the combined TX/RX pointing error (DL beam peak mismatch plus UL beam peak mismatch) is bounded. For a 32-port AAS with 3° 3dB H-beamwidth, a 15° correspondence tolerance allows the beam to land anywhere within ±5 beamwidths — generous enough for practical reciprocity calibration imperfections and thermal drift.

§15.6 — Key OTA Specifications Summary

This section consolidates the theory of §§1–15 into three complete numerical worked examples — covering DL MU-MIMO link budget, UL SRS-based reciprocity beamforming, and EIRP regulatory budget — followed by a comprehensive quick-reference table and a summary radar chart comparing 8TRX, 32TRX, and 64TRX system classes.

§16.1 — Example A: DL 16-Layer MU-MIMO at 500 m UMa NLOS

Scenario: 4 UEs, each with a rank-4 channel, located at φ = −30°, −10°, +10°, +30° in azimuth, all at 500 m distance from the gNB in Urban Macro (UMa) NLOS conditions. gNB has a 32-port AAS (8H × 4V). Carrier: 3.5 GHz (n78), 100 MHz, 30 kHz SCS, normal CP, 14 symbols per slot.

§16.2 — Example B: UL SRS-Based Beamforming (Reciprocity)

Scenario: TDD, slot pattern DDDSUUDDDD. Slot 4 is an UL slot. The gNB uses Type 6 O-RAN section (precoder-based beamforming) where the O-DU computes BFW from SRS measurements and sends them to the O-RU via eCPRI.

§16.3 — Example C: EIRP Budget for Regulatory Compliance

Given: gNB with 32TRX (32 independent TX/RX chains), each PA output power = 27 dBm, cable/connector insertion loss = 1 dB, DPD back-off = 5 dB, element gain = 8 dBi, full-array coherent combining gain = 15 dB.

§16.4 — Quick Reference Summary

Comprehensive quick-reference table of the key formulas, symbols, and numerical values for a canonical 32TRX (8H × 4V) macro AAS gNB at 3.5 GHz.

§16.5 — 8TRX / 32TRX / 64TRX System Comparison (Radar Chart)

The radar chart below compares three canonical AAS configurations on six key performance axes. Axes plotted on a linear normalised scale (0 = worst, 10 = best). Axes where smaller is better (beamwidth, fronthaul bandwidth) are inverted so that larger area always means better overall system performance.

The radar chart illustrates the fundamental engineering trade-off at each antenna configuration tier:

• 8TRX: Wide beams (low H/V-BW score), limited layers (4), but minimal fronthaul (9.0 FH score — low cost). Suitable for wide-area coverage where spatial multiplexing is secondary.
• 32TRX: Balanced profile across all six axes. Sufficient array gain (15 dB), 8-layer capability, and manageable fronthaul (~6.4 Gbps). The dominant NR Rel-15/16 macro cell configuration.
• 64TRX: Maximum array gain (18 dB), narrowest beams (best spatial resolution), highest capacity — but at the cost of high fronthaul bandwidth (12.8+ Gbps) that requires eCPRI compression or O-RAN compliant BFW offload to remain practical.