The interference graph, depicting the intra- and inter-cell interference channel gains, is indispensable for resource allocation in multi-cell networks.However, there lacks viable methods of interference graph estimation (IGE) for multi-cell multi-numerology (MN) networks. To fill this gap, we propose an efficient power-domain approach to IGE for the resource allocation in multi-cell MN networks. Unlike traditional reference signal-based approaches that consume frequency-time resources, our approach uses power as a new dimension for the estimation of channel gains. By carefully controlling the transmit powers of base stations, our approach is capable of estimating both intra- and inter-cell interference channel gains. As a power-domain approach, it can be seamlessly integrated with the resource allocation such that IGE and resource allocation can be conducted simultaneously using the same frequency-time resources. We derive the necessary conditions for the power-domain IGE and design a practical power control scheme. We formulate a multi-objective joint optimization problem of IGE and resource allocation, propose iterative solutions with proven convergence, and analyze the computational complexity. Our simulation results show that power-domain IGE can accurately estimate strong interference channel gains with low power overhead and is robust to carrier frequency and timing offsets.
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