Beam Tracking and Management

In 5G NR FR2, the SSB burst set contains up to $L = 64$ SSB beams. Each SSB occupies 4 OFDM symbols in time and 240 subcarriers (20 resource blocks) in frequency. With subcarrier spacing $\Delta f = 120$ kHz (numerology $\mu = 3$), one OFDM symbol duration is:

$$T_\text{sym} = \frac{1}{\Delta f} + T_\text{CP} = 8.33\;\mu\text{s} + 0.57\;\mu\text{s} \approx 8.9\;\mu\text{s}$$

An SSB block (4 symbols) thus spans $\approx 35.7\;\mu$s. With $L = 64$ beams multiplexed across two consecutive half-frames (5 ms each), the total SSB burst set fits within 5 ms.

The beam sweep periodicity is configurable: 5, 10, 20, 40, 80, or 160 ms. For vehicular scenarios at 100 km/h, a 20 ms periodicity is typical, corresponding to $\sim$0.56 m of displacement per sweep — well within the coherence distance at 28 GHz.

Between beam sweeps, the UE moves and the optimal beam direction changes. Rather than repeating a full sweep, beam tracking exploits temporal correlation in the angle of departure (AoD) and angle of arrival (AoA).

Model the AoD evolution as a first-order Markov process:

$$\phi[k] = \phi[k-1] + \dot{\phi}\,T_s + w[k], \qquad w[k] \sim \mathcal{N}(0, \sigma_w^2)$$

where $\dot{\phi}$ is the angular velocity and $T_s$ is the tracking interval. The extended Kalman filter (EKF) state vector is:

$$\mathbf{x}[k] = [\phi[k],\; \dot{\phi}[k],\; \alpha[k]]^T$$

where $\alpha[k]$ is the complex path gain. The measurement is the received signal power on a set of probing beams:

$$y_m[k] = |\mathbf{w}_m^H \mathbf{H}(\phi[k]) \mathbf{f}(\hat{\phi}[k|k-1])|^2 + n_m$$

The EKF prediction-update cycle maintains a running estimate $\hat{\phi}[k|k]$ with a tracking error that scales as:

$$\sigma_\phi \propto \frac{\sigma_w}{\sqrt{\text{SNR} \cdot N_\text{probe}}}$$

where $N_\text{probe}$ is the number of probing beams per tracking interval. Typically $N_\text{probe} = 2$–$4$ suffices for pedestrian speeds, while vehicular speeds may require $N_\text{probe} = 4$–$8$.

The key advantage of EKF-based tracking over periodic re-sweeping is the dramatic reduction in overhead: tracking requires $N_\text{probe}$ measurements per interval versus $N$ for a full sweep.

Beam failure occurs when the serving beam quality (L1-RSRP or L1-SINR) drops below a configured threshold $Q_\text{out}$ and remains below it for a timer duration $T_\text{BFD}$ (beam failure detection timer, typically 20–40 ms). Common causes include:

• Blockage: A pedestrian or vehicle obstructs the beam path
• Rotation: The UE rotates, placing the serving beam in a self-blockage zone
• Mobility: The UE moves outside the serving beam's coverage

The beam failure recovery (BFR) procedure in 5G NR:

1. Detection: The UE detects beam failure when $Q_\text{serving} < Q_\text{out}$ for $T_\text{BFD}$ consecutive measurement periods
2. Candidate identification: The UE selects a new candidate beam from previously measured beams with $Q_\text{candidate} > Q_\text{in}$ (the "good enough" threshold)
3. BFRQ transmission: The UE transmits a beam failure recovery request on dedicated PRACH resources (contention-free) or PUCCH, using the candidate beam direction
4. gNB response: The gNB responds on PDCCH with a beam configuration update within $T_\text{BFR}$ (typically 10–20 ms)

The total interruption time from blockage onset to beam recovery is typically 30–80 ms, during which data transmission is disrupted. Multi-panel UEs with independent beam management per panel can reduce this by maintaining backup beams on different panels.