The Caching-Sensing-Communication Tradeoff

Definition:

The (R,CRB,M)(R, \text{CRB}, M) Achievable Region

For an ISAC system with cache size MM per user, the achievable region is the set of triples (R,CRB,M)(R, \text{CRB}, M) such that:

  • Each user decodes its requested file with error ≤ϵ\leq \epsilon, requiring communication rate RR.
  • The sensing parameter θ\theta is estimated with MSE ≤CRB+δ\leq \text{CRB} + \delta.
  • Cache size MM is respected.

The region is a subset of R+3\mathbb{R}_+^3. For fixed MM, a Pareto frontier separates the (R,CRB)(R, \text{CRB}) plane.

The Pareto frontier is parametrized by ρ∈[0,1]\rho \in [0, 1]: the fraction of resources allocated to sensing. Increasing ρ\rho reduces CRB but also reduces RR. Coded caching (nonzero MM) expands the frontier compared to the uncached baseline.

Theorem: Achievable ISAC + Caching Region

Under the shared-link ISAC model with KK users, cache MM per user, total power PP, and ρ\rho fraction allocated to sensing, an achievable (R,CRB)(R, \text{CRB}) pair is R  =  (1−ρ)⋅K(1−μ)1+Kμ,CRB  =  c0ρP,R \;=\; (1 - \rho) \cdot \frac{K(1 - \mu)}{1 + K \mu}, \qquad \text{CRB} \;=\; \frac{c_0}{\rho P}, for a constant c0c_0 depending on the sensing geometry (target distance, antenna pattern, waveform).

As M→NM \to N: full cache, R=0R = 0, ρ=1\rho = 1, CRB=c0/P\text{CRB} = c_0/P (best possible sensing). As ρ→0\rho \to 0: no sensing, MAN rate.

The caching gain acts as a multiplier on the available power for communication: effectively we need only (1−ρ)/[1+Kμ](1 - \rho)/[1 + K\mu] of the raw power to deliver the same rate. The remaining power is free for sensing.

Proof
Resource allocation

Total power PP. Sensing uses ρP\rho P; communication uses (1−ρ)P(1-\rho) P.

Communication with caching

Standard MAN over a link with effective power (1−ρ)P(1-\rho)P. Rate RMAN(M)=K(1−μ)/(1+Kμ)R_\text{MAN}(M) = K(1 - \mu)/(1 + K\mu). Scaled by power fraction: (1−ρ)RMAN(1 - \rho) R_\text{MAN}.

Sensing CRB

Standard Fisher-information argument for sensing parameter θ\theta embedded in the transmitted waveform at power ρP\rho P: CRB(θ)=c0/(ρP)\text{CRB}(\theta) = c_0/(\rho P).

Joint achievability

Orthogonal allocation preserves both. Non-orthogonal schemes (superposition) can improve; proof of optimality is an open problem. ■\blacksquare

ISAC Rate-CRB Achievable Region

Achievable (sensing quality,R)(\text{sensing quality}, R) region. Pareto frontier parametrized by ρ\rho. Coded-caching curve dominates uncached baseline at every ρ\rho.

Parameters
10
0.3

Convexity of the Achievable Region

The achievable region above is convex in (R,CRB−1)(R, \text{CRB}^{-1}): the Pareto frontier is a concave curve. This follows from standard time-sharing / orthogonal-allocation arguments. Convexity matters operationally: any point on the frontier is optimal for some linear combination of objectives, so a network controller can steer the operating point via a single scalar parameter ρ\rho (or a corresponding Lagrange multiplier).

We emphasize convexity because it enables efficient runtime optimization — a key feature for real-time ISAC deployments.

Example: Walkthrough: Rate-CRB Pareto Frontier

Trace out the Pareto frontier for K=20K = 20, M/N=0.2M/N = 0.2. Identify operating points for three representative scenarios: rate-heavy, balanced, sensing-heavy.

Solution
Parameters

K=20K = 20, μ=0.2\mu = 0.2. MAN rate (at ρ=0\rho = 0): 20⋅0.8/5=3.220 \cdot 0.8 / 5 = 3.2 files/use.

Rate-heavy ($\rho = 0.1$)

R=0.9⋅3.2=2.88R = 0.9 \cdot 3.2 = 2.88. CRB =c0/(0.1P)=10c0/P= c_0/(0.1 P) = 10 c_0/P. Full data throughput, modest sensing.

Balanced ($\rho = 0.5$)

R=1.6R = 1.6. CRB =2c0/P= 2 c_0/P. Half-and-half split.

Sensing-heavy ($\rho = 0.9$)

R=0.32R = 0.32. CRB =1.11c0/P= 1.11 c_0/P. Near-best sensing, minimal data.

Operational choice

Autonomous driving: need both good data (HD maps) and good sensing (collision avoidance). Balanced or slightly-sensing-heavy. Streaming video at home: rate-heavy. Surveillance: sensing-heavy.

Common Mistake: Caching Doesn't Directly Reduce Sensing CRB

Mistake:

Concluding that caching directly improves sensing performance.

Correction:

Caching reduces the resources required for communication — freeing power/bandwidth that can be reallocated to sensing. If the system is not reallocating (e.g., sensing is on a separate hardware chain with fixed budget), caching contributes nothing to sensing.

The ISAC + caching gain requires joint resource allocation: the same power amplifier, bandwidth, or time-slot budget must be flexibly splittable between sensing and communication.

🔧Engineering Note

Implementation in 5G Advanced and 6G

Current standardization status of ISAC + caching:

  1. 3GPP Rel-17 (2022). NR sidelink and positioning enhancements enable light-ISAC functionality. No caching integration.
  2. 3GPP Rel-18/19 (2024+). Explicit ISAC study items; MEC + caching already present. Joint ISAC-MEC not standardized.
  3. ITU 6G framework (expected 2030). ISAC is a core feature; coded caching integration likely.
  4. Research prototypes. Several European projects (Hexa-X-II, RISE-6G) include caching-aware ISAC demos.

Practical bottleneck: cross-layer coordination. Sensing is typically L1/PHY; caching is L3/MEC. Unified control plane requires new interfaces.

Practical Constraints
  • •

    3GPP Rel-17: sidelink/positioning, no caching integration

  • •

    3GPP Rel-18/19: ISAC study items, MEC present, coded not yet

  • •

    6G framework: ISAC core; coded caching candidate

  • •

    Research prototypes: Hexa-X-II, RISE-6G include demos

Key Takeaway

The three-way (caching, sensing, communication) tradeoff is characterized by a convex Pareto frontier parametrized by the sensing-power fraction ρ\rho. Coded caching expands the frontier compared to the uncached baseline: at any ρ\rho, the system achieves strictly higher communication rate and better sensing CRB than without caching. The multiplier is the familiar 1+Kμ1 + K\mu caching gain.

ISAC Background and the Caching OpportunityPredictive Caching via Sensing