Ferkans — Interactive Telecom Tutor

The Pilot Budget

Classical wireless systems allocate a fixed fraction of their resources — typically 5-15% — to pilots for channel estimation. In high-mobility scenarios, this overhead is the dominant source of rate loss: at $v = 120$ km/h with 28-GHz mmWave, the channel changes fast enough that a 5% pilot budget must be refreshed 100 times per second, eating into throughput. SAC proposes to replace most pilots with sensing-derived predictions. This section quantifies the savings and identifies the regimes where they matter.

Definition:
Pilot Overhead Fraction

The pilot overhead fraction is $\eta_{\text{pilot}} \;=\; \frac{T_{\text{pilot}}}{T_{\text{pilot}} + T_{\text{data}}}$ where $T_{\text{pilot}}$ is the time (or bandwidth, or cell count) allocated to pilots and $T_{\text{data}}$ to data within a frame.

In classical comms: $\eta_{\text{pilot}} = 0.05$ - $0.15$ , chosen to yield adequate channel estimation accuracy for precoding. Higher mobility $\Rightarrow$ more frequent pilots $\Rightarrow$ larger $\eta_{\text{pilot}}$ .

In SAC: $\eta_{\text{pilot}}$ is computed based on the prediction horizon: $\eta_{\text{pilot}}^{\text{SAC}} = 1/T_{\text{pred}} \cdot \eta_{\text{pilot}}^{\text{ref}}$ . For $T_{\text{pred}} = 5$ frames: $\eta_{\text{pilot}}^{\text{SAC}} = 20\%$ of classical.

Theorem: Spectral Efficiency Gain from SAC

For a mobile UE with coherence time $T_c$ and sensing-derived channel prediction horizon $T_{\text{pred}}$ , the spectral efficiency gain over pilot-based channel estimation is $G \;=\; \frac{1 - \eta_{\text{pilot}}^{\text{SAC}}}{1 - \eta_{\text{pilot}}^{\text{classical}}} \;\approx\; \frac{1 - T_{\text{fr}}/T_{\text{pred}}}{1 - T_{\text{fr}}/T_c}.$ Consequence. When $T_{\text{pred}} \gg T_c$ (sensing is much better than coherence-based prediction), $G$ can exceed $1.3$ — a 30% gain in spectral efficiency. Vehicular scenarios with $T_{\text{pred}} = 50$ ms and $T_c = 5$ ms achieve this regime.

Coherence time $T_c$ bounds how long a classical channel estimate is valid without update. Sensing prediction horizon $T_{\text{pred}}$ bounds how long a sensing-derived estimate is valid. The ratio $T_{\text{pred}}/T_c$ is the spectral efficiency gain — how much longer SAC can coast on a single pilot versus classical. In vehicular scenarios, sensing sees the vehicle's kinematics before the channel changes (because kinematics are smoother than phase), so $T_{\text{pred}}$ exceeds $T_c$ .

Proof

Rate formula

Rate = (1 - pilot overhead) × SINR log rate. With pilot overhead $\eta_{\text{pilot}} = T_{\text{fr}}/T_{\text{horiz}}$ (one pilot per horizon), rate = $(1 - T_{\text{fr}}/T_{\text{horiz}}) \cdot R_{\text{peak}}$ .

Ratio

SAC uses $T_{\text{pred}}$ as horizon; classical uses $T_c$ . $G = (1 - T_{\text{fr}}/T_{\text{pred}})/(1 - T_{\text{fr}}/T_c)$ .

Limit

$T_{\text{pred}} \to \infty$ : $G \to 1/(1 - T_{\text{fr}}/T_c)$ . For $T_{\text{fr}}/T_c = 0.2$ (mobile scenario): $G \to 1.25$ .

Practical

Automotive mmWave with $T_{\text{pred}} = 50$ ms, $T_c = 5$ ms, $T_{\text{fr}} = 1$ ms: $G = (1 - 0.02)/(1 - 0.2) = 0.98/0.8 = 1.23$ . 23% gain. $\blacksquare$

Key Takeaway

SAC saves the most in high-mobility regimes. For pedestrian speeds ( $T_c \sim 100$ ms, $T_{\text{pred}} \sim 1$ s), the gain is $\sim 1\%$ — insignificant. For vehicular speeds ( $T_c \sim 5$ ms, $T_{\text{pred}} \sim 50$ ms), the gain is $\sim 25\%$ — substantial. For LEO ( $T_c \sim 0.1$ ms, $T_{\text{pred}} \sim 10$ ms), the gain is $\sim 100\%$ — doubling. The paradigm pays off exactly where it is most needed.

Example: Rate Comparison Across Mobility Regimes

Compare the usable data rate of classical CSI (with pilots) and SAC across three scenarios:

Pedestrian: $v = 2$ m/s, $T_c = 100$ ms at 28 GHz.
Vehicular: $v = 30$ m/s, $T_c = 10$ ms at 28 GHz.
LEO satellite: $v = 7$ km/s (relative), $T_c = 0.3$ ms at 10 GHz.

Assume peak rate 1 Gbps, frame duration 1 ms.

Solution

Pedestrian

Classical: $\eta = 1/100 = 1\%$ . Rate = 990 Mbps. SAC: $T_{\text{pred}} \sim 1$ s. $\eta = 0.1\%$ . Rate = 999 Mbps. Gain: 0.9%. Negligible.

Vehicular

Classical: $\eta = 1/10 = 10\%$ . Rate = 900 Mbps. SAC: $T_{\text{pred}} = 50$ ms. $\eta = 2\%$ . Rate = 980 Mbps. Gain: 8%. Meaningful.

LEO

Classical: $\eta = 1/0.3 = 333\%$ ... impossible! (Coherence time < frame duration: must use shorter frames or continuous pilot tracking.) With $T_{\text{fr}} = 0.1$ ms: $\eta = 33\%$ . Rate = 670 Mbps. SAC: $T_{\text{pred}} = 10$ ms (sensed from orbital mechanics + antenna beam tracking). $\eta = 1\%$ . Rate = 990 Mbps. Gain: 48%. Enabling.

Summary

SAC gain grows monotonically with mobility. At LEO scale, SAC is the difference between usable and unusable link.

Pilot Overhead Fraction vs Velocity

Plot the classical pilot overhead $\eta_{\text{pilot}}^{\text{classical}}$ (determined by coherence time) and SAC overhead $\eta_{\text{pilot}}^{\text{SAC}}$ (determined by prediction horizon) as a function of UE velocity. Carrier frequency, frame duration, and sensing SNR are sliders.

Parameters

f_0

(GHz)28

T_{\text{fr}}

(ms)1

Sensing SNR (dB)15

Theorem: SAC Break-Even Velocity

The velocity below which SAC provides no benefit over classical pilot-based comms is $v_{\text{break-even}} \;=\; \frac{c}{2 f_0 T_{\text{fr}} \cdot G_{\text{min}}}$ where $G_{\text{min}}$ is the minimum acceptable spectral efficiency gain (e.g., 5%). For 28 GHz, $T_{\text{fr}} = 1$ ms, $G_{\text{min}} = 0.05$ : $v_{\text{break-even}} \approx 10$ m/s (36 km/h).

Interpretation. SAC is the right choice for velocities above $10$ m/s at 28-GHz automotive frame rates. Below that, classical pilot-based comms is competitive. This is the operating-point boundary for deploying SAC.

Below break-even velocity, the channel changes slowly enough that a single pilot's information lasts many frames — classical CSI is fine. Above break-even, the channel changes faster than pilots can track, and sensing-based prediction becomes essential. The break-even point is a design parameter: at 28 GHz mmWave, it's 36 km/h (urban), so essentially all vehicular deployments need SAC.

Proof

Rate inequality

SAC beats classical iff $(1 - T_{\text{fr}}/T_{\text{pred}}) / (1 - T_{\text{fr}}/T_c) \geq 1 + G_{\text{min}}$ .

Manipulation

Substituting $T_c = \lambda/(2 v)$ : $T_{\text{fr}} \cdot 2 v / \lambda \leq G_{\text{min}} \cdot (1 - T_{\text{fr}}/T_c - G_{\text{min}})$ Simplifying: $v \leq \lambda / (2 T_{\text{fr}} G_{\text{min}}) = c/(2 f_0 T_{\text{fr}} G_{\text{min}})$ . $\blacksquare$

🔧Engineering Note

Deployment Strategy: Hybrid SAC + Pilots

Practical SAC deployments use a hybrid approach:

Cold start: A few pilots at connection initiation to establish the channel and bootstrap the sensing track.
Steady state: Predicted channel drives precoder; occasional sparse pilots (1-2 per 10 frames) refresh the state estimate.
Maneuver events: Detected by the sensing subsystem (large acceleration innovation); triggers immediate pilot refresh
- model switch (CV → CA or IMM).
Link handover: When switching beams or cells, dense pilots re-bootstrap the new link.

This hybrid saves $\sim 60$ - $75\%$ of pilot overhead compared to fixed-rate pilot schemes, without compromising link robustness. 5G NR and 6G proposals for vehicular scenarios are expected to adopt variants of this strategy.

Practical Constraints

•
Bootstrap with pilots at connection start
•
Steady-state: 1-2 pilots per 10 frames
•
Maneuver trigger: immediate pilot refresh
•
Handover: dense pilot re-bootstrap

Pilot-Based vs SAC Channel Estimation

Property	Classical Pilot-Based	SAC (Sensing-Based)
Overhead	5-15% of resources	1-3% of resources
Channel freshness	Always 1 frame old	Prediction up to $T_{\text{pred}}$
Mobility support	Up to $\sim 300$ km/h	Up to LEO speeds
Compute	O(MN) per frame	O(MN·P·N_r) per frame (sensing)
Cold-start	Rapid (1 pilot)	Needs 2-3 frames to bootstrap
Robustness to sensing failure	N/A	Falls back to pilot-based
Spectral efficiency gain	0% (baseline)	5-30% (mobility-dependent)

Common Mistake: SAC Covers Path Parameters, Not Gains

Mistake:

Assuming SAC eliminates pilots entirely. Sensing estimates path delays, Dopplers, and angles; the complex path gains $a_i$ must be re-estimated, since they encode small-scale fading that sensing cannot resolve.

Correction:

Use SAC for the structural parameters (geometry) and occasional pilots for the gain parameters $a_i$ . One reference symbol per frame ( $\sim 0.5\%$ overhead) is sufficient to track the $P$ gains — a massive reduction from classical 10% overhead for all channel parameters. The SAC win is in eliminating the geometric estimation, not the small-scale fading.

Why This Matters: Connection: Cell-Free Massive MIMO (Ch 17)

Chapter 17 extends SAC to cell-free massive MIMO: each AP runs its own sensing subsystem, and sensing outputs are shared across APs to predict UE channels from multiple geometric viewpoints. This cell-free SAC is especially powerful because the APs are distributed — different APs see different paths — so the aggregated target scene is richer than any single AP can produce. The quantitative gain at cell-free scale: $\sim 40\%$ additional throughput beyond single-cell SAC.

Pilot-Overhead Reduction via Sensing