Why more antennas help
A single antenna radiates energy in all directions — only a tiny fraction reaches the intended UE. An array of antennas, each transmitting the same signal with carefully chosen phase offsets, creates constructive interference in the desired direction and destructive interference in all other directions. This is a beam.
With N antennas, the maximum beamforming gain is N times the single-antenna power in the beam direction. For a 64-antenna array: 18 dB gain. This is why 5G can operate at higher frequencies (more path loss) and still achieve good coverage.
Beamforming mathematics
Consider a uniform linear array (ULA) of N antennas spaced half a wavelength apart. To steer a beam at angle θ from broadside, the signal at antenna n is delayed by n × (d/λ) × sin(θ) wavelengths, equivalent to a phase shift.
// Uniform Linear Array (ULA) steering vector: d = λ/2 (half-wavelength spacing) θ = 30° (desired beam direction) // Phase shift per element: ψ = 2π × (d/λ) × sin(θ) = 2π × 0.5 × sin(30°) = 2π × 0.5 × 0.5 = π/2 radians // Beamforming weight vector w (N=8): w = [1, e^(jπ/2), e^(jπ), e^(j3π/2), e^(j2π), e^(j5π/2), e^(j3π), e^(j7π/2)] = [1, j, -1, -j, 1, j, -1, -j] // Array gain at θ=30°: |w^H × a(θ)|² = N² = 64 (8² = 18 dB gain) // Array gain at θ=60° (interference null): |w^H × a(60°)|² ≈ 0.02 (−17 dB nulling)
Precoding — connecting beamforming to 3GPP
In 3GPP, beamforming is implemented through precoding. The gNB multiplies the data symbols by a precoding matrix W before transmitting from multiple antenna ports. The UE reports a Precoding Matrix Indicator (PMI) — an index into a codebook of predefined precoding matrices — telling the gNB which precoder it prefers.
CSI feedback — how the gNB learns the channel
The gNB transmits CSI-RS (Channel State Information Reference Signals) — known pilot signals from specific antenna ports. The UE measures these, estimates the channel, and reports back:
| Report | Full name | Description | Bits |
|---|---|---|---|
| CQI | Channel Quality Indicator | Recommended MCS index (0–15) | 4 |
| PMI | Precoding Matrix Indicator | Best precoder from codebook | varies |
| RI | Rank Indicator | Number of spatial layers (1–4) | 1–2 |
| LI | Layer Indicator | Best layer for single-layer PDSCH | varies |
| CRI | CSI-RS Resource Indicator | Best CSI-RS beam (for SSB beam management) | varies |
Spatial multiplexing — multiple layers
With enough antenna elements and sufficient scattering in the environment, the gNB can transmit multiple independent data streams (layers) simultaneously to the same UE. This is spatial multiplexing. The maximum number of layers equals the minimum of the number of transmit and receive antennas and the channel rank.
For our UE: RI=1 (single layer reported). If RI=2, the throughput doubles — 2 independent streams occupy the same time-frequency resources.