Ferkans — Interactive Telecom Tutor

Scheduling in the Future

Sections 2-4 showed how to predict channels and beams a few frames ahead. The natural next step is to use those predictions to schedule resources — not just for the next frame, but for the next 10-100 frames. Predictive resource allocation (PRA) exploits the short-horizon channel forecast to pre-allocate power, time, and frequency — improving fairness, reducing latency, and enabling URLLC-style guaranteed-service without constant re- planning. This section formalizes PRA and shows how it interacts with the SAC framework.

Definition:
Predictive Resource Allocation (PRA)

Predictive resource allocation is the decision of resource blocks (time, frequency, spatial streams) over a horizon of $T_{\text{pred}}$ frames, using channel predictions $\{\hat{\mathbf{h}}^{(t+\tau)}\}_{\tau=1}^{T_{\text{pred}}}$ as inputs.

The PRA problem for $K$ users over horizon $T_{\text{pred}}$ is $\begin{aligned} \max_{\{\mathbf{p}^{(\tau)}\}, \{\mathbf{F}^{(\tau)}\}} \;&\; \sum_{\tau=1}^{T_{\text{pred}}} \sum_{k=1}^{K} U_k(\rho_k^{(\tau)}) \\ \text{s.t.} \;&\; \rho_k^{(\tau)} \leq \log(1 + \mathrm{SINR}_k^{(\tau)}), \quad \text{power},\text{rate constraints} \end{aligned}$ where $U_k$ is user $k$ 's utility function, $\rho_k^{(\tau)}$ is the rate allocated to user $k$ at frame $\tau$ , and $\mathbf{F}^{(\tau)}$ is the precoder.

Theorem: PRA as a Two-Stage Problem

The PRA problem decomposes into:

Per-frame precoder design: given $\hat{\mathbf{h}}^{(\tau)}$ , find $\mathbf{F}^{(\tau)}$ and spatial resource allocation. This is the Ch. 13 joint beamforming problem.
Temporal smoothing: allocate power and users across frames to optimize $\sum_\tau U_k(\rho_k^{(\tau)})$ . This is a convex dynamic program.

Consequence. PRA solvers can reuse the Ch. 13 per-frame beamformer, then add a lightweight temporal optimization on top. The combined complexity is a few times the per-frame cost — well within 5G/6G scheduler budgets.

PRA's power is in the temporal stitching: a user on a bad channel this frame may have a good channel two frames ahead (because of sensing-predicted beam realignment). A myopic scheduler misses this; PRA exploits it. The temporal optimization is a classical dynamic program over a short horizon — easy to solve if the channel predictions are good.

Proof

Decomposition

Given $\{\hat{\mathbf{h}}^{(\tau)}\}$ , the optimal $\mathbf{F}^{(\tau)}$ depends only on $\hat{\mathbf{h}}^{(\tau)}$ (no inter-frame coupling in the precoder). Temporal optimization stitches per-frame results.

Temporal sub-problem

Fix $\mathbf{F}^{(\tau)}$ ; optimize power/user allocation via convex DP. Cost: $\mathcal{O}(K T_{\text{pred}})$ per iteration, $\mathcal{O}(\log(1/\epsilon))$ iterations for ADMM/proximal methods.

Convergence

Per-frame design is convex (Ch. 13); temporal is convex. Joint problem is convex, solved globally. $\blacksquare$

Definition:
URLLC Latency-Reliability via PRA

Ultra-reliable low-latency communication (URLLC) requires $99.999\%$ probability of meeting a latency bound (e.g., 1 ms). Classical schedulers must reserve worst-case resources; PRA can do better.

PRA for URLLC: Predict channel for the next $T_{\text{pred}}$ frames. Reserve exactly enough resources to achieve target reliability over that window, not perpetually. Adjust reservation each frame as predictions update.

Benefit: Reservation size $\sim T_{\text{pred}}/T_{\text{total}}$ smaller than classical. For $T_{\text{pred}} = 10$ ms and $T_{\text{total}} = 100$ ms URLLC window: 10× less reservation. Frees 90% of reserved capacity for other (non-URLLC) users.

Theorem: URLLC Reservation Fraction

For URLLC users requiring latency $T_{\text{URLLC}}$ and reliability $1 - \epsilon$ , the fraction of resources that must be reserved is $\eta_{\text{URLLC}} \;=\; \max\!\left(\frac{T_{\text{URLLC}}}{T_{\text{pred}}}, \frac{-\log\epsilon}{\log(1/\eta_0)}\right)$ where $\eta_0$ is the worst-case per-frame reservation fraction without prediction. With SAC predictions of horizon $T_{\text{pred}} = 5$ ms and URLLC latency $T_{\text{URLLC}} = 1$ ms: $\eta_{\text{URLLC}} \;=\; \max(0.2, -\log \epsilon/\log \eta_0^{-1}),$ which for $\epsilon = 10^{-5}$ , $\eta_0 = 0.2$ : $\eta_{\text{URLLC}} \approx 20\%$ (vs $100\%$ for worst-case reservation).

Consequence. SAC enables a $5\times$ reduction in URLLC reservation. A 5G NR system with URLLC and eMBB slices, both served by the same BS, can dedicate 80% more capacity to eMBB with SAC — roughly doubling effective BS throughput.

URLLC reservation without prediction is a worst-case calculation: reserve enough to meet the latency budget even under the worst possible channel. With prediction, the worst-case is known in advance, so only the frames where the channel is bad get dedicated reservation. Good-channel frames are released to other users. The prediction horizon $T_{\text{pred}}$ bounds the look- ahead; shorter horizons require more hedging.

Proof

Worst-case bound

Reliability: $\mathbb{P}(R \geq R_{\text{min}} \text{ for all frames}) \geq 1 - \epsilon$ . Classical: reserve worst-case over $T_{\text{URLLC}}/T_{\text{fr}}$ frames.

PRA bound

Reserve worst-case over $T_{\text{pred}}/T_{\text{fr}}$ frames. Remainder: opportunistic use by other users.

Combined

$\eta = T_{\text{URLLC}}/T_{\text{pred}}$ if prediction is reliable, plus safety margin. $\blacksquare$

PRA: Joint Temporal-Spatial Solver

Input: Channel predictions {ĥ^(τ)} for τ = 1..T_pred

User utility functions {U_k}

Power budget P_t per frame, reservation fraction η_URLLC

Output: Schedule {R_k^(τ)}, precoders {F^(τ)}

Initialization:

Per-frame: F^(τ) = MRT precoder to each user on ĥ^(τ).

Temporal: R_k^(τ) = log(1 + SINR_k(F^(τ))).

Repeat until convergence:

1. TEMPORAL UPDATE:

Fix {F^(τ)}. Re-allocate rates to maximize Σ U_k:

proximal gradient on utility

enforces power budget per frame

2. PRECODER UPDATE:

Fix {R_k^(τ)}. Solve per-frame precoding SDP:

max sum rate subject to target rates and power

Use Ch. 13 covariance SDP solver.

3. CONVERGENCE CHECK:

If ||schedule change|| < ε: return

Else: increment iteration.

Typical: 3-5 iterations to convergence. Per iteration:

O(T_pred × N_t^3) for precoder + O(K × T_pred) for temporal.

Example: Urban PRA: eMBB + URLLC

A BS serves 20 eMBB users (high throughput, delay-tolerant) and 4 URLLC users (low rate, low latency) at 28 GHz. Each URLLC user needs 1 Mbps with 1-ms latency and $10^{-5}$ reliability. Sensing horizon $T_{\text{pred}} = 50$ ms.

(a) Compare URLLC reservation: classical vs PRA. (b) Estimate eMBB capacity gain. (c) State handover detection window.

Solution

Classical URLLC reservation

Must dedicate enough capacity for 4 URLLC users under worst- case channel. ~20% of BS capacity reserved continuously.

PRA URLLC reservation

Reserve 20% × (1 ms / 50 ms) = 0.4% of capacity continuously; additional reservation in predicted bad-channel frames: ~5% peak. Average: ~2.5%.

eMBB gain

Capacity freed: 17.5% (from 20% baseline to 2.5% PRA). eMBB users get $\sim 20\%$ more throughput. Significant at cell edge where capacity is scarce.

Handover detection

Sensing sees URLLC UE approaching cell edge at 10-20 m/s. For a 50-m cell: $T_{\text{HO}} = 50/10 = 5$ s. Orders of magnitude better than classical handover detection.

Summary

PRA + SAC delivers 20% eMBB gain + 5-10× better URLLC reservation efficiency + 5-second handover warning. Operational URLLC failure rate drops from 0.01% to < 0.001%.

URLLC Reservation: Classical vs PRA

Plot the URLLC reservation fraction as a function of prediction horizon. Compare classical (no prediction), short-horizon PRA ( $T_{\text{pred}} = 1$ ms), and long-horizon SAC-PRA ( $T_{\text{pred}} = 50$ ms). Sliders: user count, URLLC latency target, reliability target.

Parameters

URLLC users4

URLLC latency (ms)1

Reliability (

10^{-k}

)5

🎓CommIT Contribution(2023)

Predictive Resource Allocation for SAC

Y. Zhao, F. Liu, G. Caire — IEEE Trans. Wireless Communications

The CommIT contribution to PRA unifies SAC (Chapters 14 §1-4) with multi-user scheduling. The paper establishes:

Two-stage decomposition: per-frame precoder + temporal optimization (Theorem 14.13).
URLLC reservation reduction: sensing horizon enables 5× less reservation for $10^{-5}$ -reliability URLLC (Theorem 14.15).
Convex dynamic program: PRA over the sensing horizon is a convex DP — tractable on commercial schedulers.

Together, the Liu-Caire 2022 (joint beamforming), Cui-Yuan-Caire 2023 (tracking), and Zhao-Liu-Caire 2023 (PRA) papers form a complete CommIT framework for sensing-assisted communication. The operational gains — 20-30% eMBB throughput + 5× URLLC efficiency — are a direct consequence of the DD-domain sparsity and the sensing-comms feedback loop.

commitpraurllcsac

🔧Engineering Note

PRA in Commercial Schedulers

Commercial 5G/6G schedulers need to integrate PRA without sacrificing the instant-scheduling properties that serve mixed- load traffic. The path forward:

Layered scheduler: Fast myopic scheduler (MUCH simpler than PRA) handles per-frame decisions. PRA runs at slot granularity (10 ms), providing resource-allocation hints.
Hint-based dispatch: Fast scheduler uses PRA hints as priorities; can override if the myopic context requires it.
Fallback: If PRA hints are inconsistent (sensing failure), fast scheduler operates autonomously.

This architecture preserves the benefits of PRA (5× URLLC efficiency) without sacrificing the responsiveness of the fast scheduler. 6G standardization is considering PRA as a deployment option; 5G NR already supports "predictive" hints at the RAN level, though not yet through sensing.

Practical Constraints

•
Two-layer: fast myopic + slow PRA (at slot granularity)
•
Hint-based: PRA informs myopic, doesn't dictate
•
Fallback: myopic alone if PRA fails

Why This Matters: Chapter 15: V2X — The Flagship Application

This chapter developed SAC and PRA in abstract terms. Chapter 15 applies them to automotive V2X (vehicle-to-everything) scenarios — the single most demanding application for the SAC-PRA framework. V2X requires sub-millisecond latency (URLLC), cm-level accuracy (sensing), and 100+ km/h mobility (high prediction horizon demand). The OTFS-SAC-PRA stack, developed in Chapters 12-14, hits all these requirements simultaneously — no other waveform approach does. Chapter 15 demonstrates this with concrete cooperative-perception and platooning designs.

Predictive Resource Allocation