Ferkans — Interactive Telecom Tutor

Beam Management at mmWave Speeds

mmWave links are narrow-beam: a 28-GHz BS with $N_t = 64$ antennas has a 3-dB beamwidth of $\sim 2°$ . A moving UE — a pedestrian, a vehicle, a UAV — traverses this beamwidth in milliseconds. Without continuous beam tracking, the link breaks. Classical beam management uses exhaustive beam sweeps (SSB in 5G NR), which consume substantial overhead. SAC provides a principled alternative: the sensing subsystem tracks the UE's position and velocity, and the beam is steered to the predicted direction at each frame. This section formalizes the beam prediction problem and quantifies its gains.

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Definition:
mmWave Beam Codebook

The BS-side mmWave beam codebook $\mathcal{B}_{\text{comms}}$ is a set of $|\mathcal{B}_{\text{comms}}| = L$ precoder vectors $\{\mathbf{f}_\ell\}_{\ell=1}^L$ covering the angular domain. Typical designs:

Uniform angular: $\mathbf{f}_\ell = \mathbf{a}_t(\phi_\ell)/\|\mathbf{a}_t(\phi_\ell)\|$ , with angles $\phi_\ell$ uniformly spaced over $[-\pi/2, \pi/2]$ . $L = 2 N_t$ typical.
Hierarchical: coarser beams on one level, finer on next. Enables coarse-to-fine search.
Codebook-aware: jointly designed with sensing codebook $\mathcal{B}_{\text{sense}}$ so that joint beamforming reuses array resources.

Beam selection problem: given the estimated user direction $\hat\phi$ (from sensing), select $\hat\ell = \arg\max_\ell |\mathbf{a}_t(\hat\phi)^H \mathbf{f}_\ell|$ . Uses the sensing estimate directly, no beam-sweep required.

Theorem: Beam Prediction Gain

For a mobile UE with angular velocity $\dot\phi$ and prediction horizon $T_{\text{pred}}$ , the probability that the sensing-predicted beam is correct is $P_{\text{correct}} \;=\; \Phi\left(\frac{B/2 - |\dot\phi| T_{\text{pred}}}{\sigma_\phi}\right)$ where $B$ is the beamwidth, $\dot\phi T_{\text{pred}}$ is the angular drift over the prediction window, and $\sigma_\phi$ is the sensing angle CRB.

Consequence. For automotive mmWave with $B = 4°$ , $\dot\phi = 0.1$ rad/s, $T_{\text{pred}} = 50$ ms, $\sigma_\phi = 1°$ : $P_{\text{correct}} \approx 95\%$ — far beyond pilot-based beam tracking under the same conditions.

Beam prediction fails when either (a) the UE has moved to a different beam, or (b) the sensing estimate was wrong to begin with. Both are separable: the former depends on UE kinematics and prediction horizon, the latter on sensing SNR. By keeping $T_{\text{pred}}$ short (frequent updates) and sensing SNR high, prediction succeeds with high probability, obviating beam-sweep.

Proof

Error model

Predicted angle error: $\hat\phi^{(t+T)} - \phi^{(t+T)} = (\hat\phi^{(t)} - \phi^{(t)}) + \dot\phi T + \mathcal{O}(\text{higher order})$ . First term: sensing error. Second: kinematic drift.

Beam boundary

Beam $\ell$ covers $[\phi_\ell - B/2, \phi_\ell + B/2]$ . Beam is correct iff $|\hat\phi^{(t+T)} - \phi^{(t+T)}| \leq B/2$ .

Gaussian approximation

Error distribution: $\mathcal{N}(\dot\phi T, \sigma_\phi^2)$ . $P_{\text{correct}} = \mathbb{P}(|\text{error}| \leq B/2) = \Phi((B/2 - \dot\phi T)/\sigma_\phi)$ . $\blacksquare$

Sensing-Assisted Beam Tracking

Input: Current frame t, beam codebook B_comms,

Current UE track (position, velocity, angle)

Prediction horizon T_pred frames

Output: Beam index for frame t+1

1. PREDICT:

φ̂^{(t+1|t)} = φ̂^{(t)} + φ̇^{(t)} · T_fr

σ_φ² = CRB(φ̂^{(t+1|t)})

2. SELECT BEAM:

ℓ^* = argmax_ℓ |a_t(φ̂^{(t+1|t)})^H f_ℓ|²

3. VERIFY (at t+1):

After receiving frame t+1, compute innovation:

e = z̃^{(t+1)} - ẑ^{(t+1|t)}

If ||e||_Σ > γ_switch: BEAM MISMATCH

→ Initiate beam-sweep, update track, resume

Else: continue with ℓ^* for next frame

4. PERIODIC REFRESH:

Every N_refresh frames, run a light beam-sweep to verify.

N_refresh = 50 typical at 100 Hz (= 0.5 s).

Complexity: O(L) per frame beam selection; O(1) per frame in

steady state; O(L) + O(MN) during beam-sweep events.

Example: Automotive Beam Tracking with SAC

A 28-GHz BS tracks a vehicle on a curved road (angular velocity $\dot\phi = 0.2$ rad/s). Beamwidth $B = 3°$ . Sensing CRB on angle: $\sigma_\phi = 0.8°$ . Frame rate 100 Hz ( $T_{\text{fr}} = 10$ ms).

(a) Compute the angular drift per frame. (b) Using Thm. 14.9, compute the prediction reliability. (c) Determine the maximum pilot-free interval.

Solution

Angular drift

$\dot\phi T_{\text{fr}} = 0.2 \cdot 0.01 = 2 \times 10^{-3}$ rad = $0.11°$ . Well below beamwidth; drift alone won't cause beam miss.

Prediction reliability

$P_{\text{correct}} = \Phi((B/2 - \dot\phi T_{\text{fr}})/\sigma_\phi) = \Phi((1.5 - 0.11)/0.8) = \Phi(1.74) = 96\%$ . Vast majority of frames: correct beam.

Pilot-free interval

For $P_{\text{correct}} \geq 95\%$ : $T_{\text{pred}}$ up to $(B/2 - 1.64 \sigma_\phi)/\dot\phi = (1.5 - 1.3)/11.4 \approx 0.02$ s = 2 frames.

Summary

2-frame prediction with 95% reliability. Light pilot refresh every 5-10 frames for safety. Overhead: $\sim 2\%$ vs classical 10%.

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Beam Prediction Accuracy vs Horizon

Plot $P_{\text{correct}}$ as a function of prediction horizon, for multiple angular velocities. Horizontal bars show common frame rates (100 Hz, 500 Hz, 1 kHz). Sliders: sensing SNR, beamwidth.

Parameters

Angular vel (°/s)10

Beamwidth (°)3

Sensing

\sigma_\phi

(°)0.8

Theorem: Handover Detection via Sensing

A UE approaching a cell boundary can be detected from sensing $T_{\text{HO}}$ frames before the actual handover event, where $T_{\text{HO}} \;=\; \frac{d_{\text{boundary}} - \sigma_d}{v_{\text{radial}}}.$ Here $d_{\text{boundary}}$ is the distance to the cell boundary, $\sigma_d$ is the sensing range uncertainty, and $v_{\text{radial}}$ is the UE's radial velocity.

Consequence. For a UE 50 m from the boundary at 30 m/s, $T_{\text{HO}} \approx 1.6$ s — ample time to prepare the handover (signal the new BS, pre-compute beams, etc.). Classical HO based on signal-strength measurements has only 100-300 ms warning — 5-10× less. Early warning reduces handover failures and dropped calls.

Classical handover is triggered when the received signal drops; by then, the UE is already near the boundary. Sensing-based handover detects the UE approaching the boundary well in advance, using position + velocity. This transforms handover from a reactive event to a planned one — a significant reliability improvement, especially at high mobility.

Proof

Kinematic approach

UE position at time $t$ : $d(t) = d_0 - v_{\text{radial}} t$ . Boundary reached when $d(t) = 0$ : $t = d_0/v_{\text{radial}}$ .

Warning time

Sensing detects UE within $\sigma_d$ of boundary: $T_{\text{HO}} = (d_0 - \sigma_d)/v_{\text{radial}}$ . $\blacksquare$

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🔧Engineering Note

SAC Beam Management in 5G NR / 6G

Current 5G NR uses periodic SSB (synchronization signal block) beam-sweep every 20 ms at mmWave bands. This is ~10% overhead for beam management.

SAC-based beam management replaces most SSB sweeps with sensing-derived beam prediction. 5G NR beam-sweep becomes:

Initial attach: full sweep (bootstrap).
Mobility: sensing-driven (1-2% overhead).
Handover: 5G NR measurement framework (pre-notified by sensing, so prepared).

6G proposals (3GPP TR 38.913 beyond-5G) explicitly include sensing-based beam management. Expected standardization: 2028-2030. Compatibility with 5G NR achieved by running SAC as an optional layer above SSB.

Practical Constraints

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Bootstrap: full beam-sweep at initial attach
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Steady-state: sensing-driven (1-2% overhead)
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Handover: early warning from sensing
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6G standardization 2028+

Common Mistake: LOS-NLOS Transitions Break Prediction

Mistake:

Assuming the sensing-based beam prediction is always correct when the UE transitions from a line-of-sight (LOS) path to a reflected (NLOS) path. The dominant AoA changes discontinuously; prediction fails even though kinematics are smooth.

Correction:

Detect NLOS transitions by monitoring the spatial covariance $\mathbf{R}_y = \mathbb{E}[\mathbf{y}\mathbf{y}^H]$ . Sudden rank increase or shift in dominant direction signals the transition. Fall back to beam-sweep on detection. In urban environments, LOS-NLOS transitions happen at $\sim 1$ -Hz rate; prediction success rate falls to $\sim 70\%$ during such transitions. Mitigation: multi-path beam tracking (track top-3 paths, not just dominant) retains beam on path 2 or 3 during transition.

Beam Prediction and Tracking