Sparse Spectrum Reuse in HetNets with Relays

In-band relay nodes (RNs) can be utilized to enhance the coverage of heterogeneous networks (HetNets) in a cost-effective way. However, the in-band RNs also consume the limited spectrum resources. Appropriate spectrum resource management/cooperation is necessary to ensure the balanced resource usages between the macro base stations (BSs) and the RNs. In this paper, we study the sparse spectrum reuse strategy in a HetNet with in-band RNs to maximize the overall proportional fairness metric. Although limiting the number of active reuse patterns will degrade the performance and render the resulting problem non-convex, we first show that there must exist one solution achieving the optimum when the upper bound on the number of active reuse patterns is not less than the total number of mobile stations (MSs) and RNs. We also put forth one active pattern identification scheme based on the re-weighted $\ell_1$-norm algorithm to deal with the non-convex problem and refine the set of active reuse patterns in a soft manner. Furthermore, in order to offload the heavy computation burden from the central server, one distributed resource allocation algorithm based on the alternating direction method of multipliers (ADMM) algorithm is developed. Numerical simulations demonstrate the superiority and effectiveness of our proposed algorithm.