Update Strategy for Channel Knowledge Map in Complex Environments

TL;DR

This work tackles the problem of when to update Channel Knowledge Maps (CKMs) in dynamic 6G environments by introducing a Map Efficacy Function (MEF) that captures both aging and environmental shifts. It formulates CKM update scheduling as a fractional programming problem and presents two Dinkelbach-based solutions, Delta-P (globally optimal on discrete schedules) and Delta-L (near-linear, linearized inner optimization), along with a threshold policy for unpredictable environments. For predictable environments, the approach yields long-term trajectories that align updates with segment boundaries and varying costs, revealing that rapid environmental decay and strong entry loss favor immediate updates while slow decay and weak loss favor delay. Simulation demonstrates that Delta-P achieves the theoretical Pareto frontier and Delta-L closely tracks it, offering substantial reductions in updates with minimal MEF loss, thereby enabling practically efficient CKM maintenance in complex wireless environments.

Abstract

The Channel Knowledge Map (CKM) maps position information to channel state information, leveraging environmental knowledge to reduce signaling overhead in sixth-generation networks. However, constructing a reliable CKM demands substantial data and computation, and in dynamic environments, a pre-built CKM becomes outdated, degrading performance. Frequent retraining restores accuracy but incurs significant waste, creating a fundamental trade-off between CKM efficacy and update overhead. To address this, we introduce a Map Efficacy Function (MEF) capturing both gradual aging and abrupt environmental transitions, and formulate the update scheduling problem as fractional programming. We develop two Dinkelbach-based algorithms: Delta-P guarantees global optimality, while Delta-L achieves near-optimal performance with near-linear complexity. For unpredictable environments, we derive a threshold-based policy: immediate updates are optimal when the environmental degradation rate exceeds the resource consumption acceleration; otherwise, delay is preferable. For predictable environments, long-term strategies strategically relax these myopic rules to maximize global performance. Across this regime, the policy reveals that stronger entry loss and faster decay favor immediate updates, while weaker entry loss and slower decay favor delayed updates.

Figures (5)

• Figure 1: Evolution of AoI and MEF over update cycles.
• Figure 2: Illustration of the threshold-based update strategy. The horizontal axis represents the acceleration of computational resource consumption ($\frac{C}{D^2}$), while the vertical dashed line denotes the threshold determined by the environmental change rate ($-\frac{f^{\prime}(0)}{2}$). The zero-wait policy is optimal only when the acceleration of computational resource consumption is lower than the rate of environmental degradation.
• Figure 3: Pareto frontier of working time $G$, efficacy $F$, and update cost $C_{tot}$.
• Figure 4: Comparison of Delta-L with baseline update policies. Delta-L optimally aligns updates with segment boundaries and fast-decay periods, achieving higher objective value $J$ than Zero-wait, Fixed-10m, and Fixed-25m baselines.
• Figure 5: Trade-off between average MEF and update cost, where the color of each point indicates its objective value.

Theorems & Definitions (24)

• Lemma 1: Two-parameter Dinkelbach equivalence
• proof
• Definition 1: Dominance, nondominance, Pareto frontier
• Lemma 2: Dominance preserved under extension
• proof
• Lemma 3: Safety of dominance pruning
• proof
• Lemma 4: Completeness invariant
• proof
• Theorem 1: Completeness of the terminal frontier