Physics-grounded Mechanism Design for Spectrum Sharing between Passive and Active Users

Abstract

We propose a physics-grounded mechanism design for dynamic spectrum sharing that bridges the gap between radiometric retrieval constraints and economic incentives. We formulate the active and passive users coexistence problem as a Vickrey-Clarke-Groves (VCG) auctions mechanism, where the radiometer dynamically procures ``quiet'' time-frequency tiles from active users based on the marginal reduction in retrieval error variance. This approach ensures allocative efficiency and dominant-strategy incentive compatibility (DSIC). To overcome the computational intractability of exact VCG on large grids, we derive an approximation algorithm by using the monotone submodularity induced by the radiometer equation. AMSR-2-based simulations show that the approach avoids high-cost tiles by aggregating low-cost spectrum across time and frequency. In an interference-trap case study, the proposed framework reduces procurement costs by about 60% over a fixed-band baseline while satisfying accuracy targets.

Figures (4)

• Figure 1: Comparison of coexistence paradigms on a discretized time–frequency grid with three channels. (Top) Regime 1: Static Partitioning. The 23.8 GHz band (Ch 1) is permanently allocated to passive sensing (blue), resulting in the complete exclusion of active users in this band regardless of their costs. (Middle) Regime 2: Time-Dynamic Sharing. Spectrum access is regulated by a fixed integration window $\tau$. All channels are silenced simultaneously during the overpass, blocking high-value active users in Ch 2 and Ch 3 while failing to use low-cost periods outside the window. (Bottom) Regime 3: Fully Flexible Sharing (Proposed). The market-based mechanism dynamically selects a subset of tiles with the lowest opportunity costs (lightest red background) scattered across the grid.
• Figure 2: Simulation Setup: Commercial Opportunity Cost Field ($15 \times 20$ grid). The heatmap displays the opportunity cost for each time--frequency tile. The dashed blue lines delineate the three radiometric channels. A high-cost "Interference Trap" (dark red, high cost) is considered in the highly sensitive 23.8 GHz band to test the mechanism's ability to navigate spectral congestion.
• Figure 3: Micro-Dynamics of Market Clearing in the 23.8 GHz Channel. The blue curve illustrates the radiometer's marginal valuation density ($v \propto 1/B^2$), exhibiting diminishing returns. The red steps represent the sorted opportunity costs of active users. The mechanism reaches equilibrium at $Q = 70$ tiles. Note that the equilibrium marker is positioned at the cost of the first rejected tile ($P \approx \$51$). This point illustrates the impact of the "Interference Trap": the mechanism effectively purchases low-cost background spectrum and autonomously stops procurement precisely when the opportunity cost of the subsequent tile exceeds the marginal scientific value.
• Figure 4: Computational scalability and efficiency. Left: Execution time (log scale) versus the grid size $|\Omega|$. The optimal solver grows exponentially with ($|\Omega|)$) in our implementation, reaching 25 seconds for $|\Omega|=21$. The proposed Scalable Posted-Price Greedy Algorithm (green) scales approximately linearly over the tested grid sizes, solving instances in microseconds. Right: Optimality gap (percentage cost overrun relative to the global optimum). The greedy solution achieves a mean optimality gap of 4.45%.

Theorems & Definitions (5)

• Theorem 4.1
• proof
• Proposition 5.1: Monotone Submodularity
• proof
• Theorem 5.1