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In-band relay nodes can be utilized to enhance the coverage of heterogeneous networks in a cost-effective way. However, the wireless backhaul links of in-band relay nodes also consume the limited spectrum resources. Appropriate spectrum resource management/cooperation is necessary to ensure the balanced resource usages between the macro base stations and the relay nodes. In this paper, we derive an optimal spectrum reuse strategy in a heterogeneous network with in-band relay nodes to maximize the overall proportional fairness metric. We first provide one distributed resource allocation algorithm based on the alternating direction method of multipliers for the heterogeneous network with in-band relay nodes. Even though the number of feasible spectrum reuse patterns increases exponentially with the total number of base stations and relay nodes, we further prove that we can achieve the optimal network performance by only activating a limited number of spectrum reuse patterns, which is just in the order of the total number of mobile stations and relay nodes. According to this finding, we put forth an algorithm to refine the set of active reuse patterns in a soft manner by employing the re-weighted <inline-formula> <tex-math notation="LaTeX">$\ell _{1}$ </tex-math></inline-formula>-norm algorithm. Numerical simulations demonstrate the superiority and effectiveness of our proposed algorithms.

Optimal Frequency Reuse in HetNets With In-Band Relays