Optimal power control in two-tier networks at low-SNR regime

This paper considers optimum uplink power control policy that maximizes system capacity without any interference cancellation techniques for HetNets or cognitive-radio (CR) networks at low-SNR regime. System model has two-tier to cover cognitive-radio and heterogenous networks structures. Tier 2 users cause interference on tier 1 user under spectrum sharing paradigm. In proposed scenario, this interference power on tier 1 user is limited at a certain level. The objective function of power optimization problem is changed with an upper bound function to find optimum power control policy under individual peak power constraint at Tier2s and total interference constraint at Tier1 for uplink case at low-SNR regime. To this end, two optimal solutions, one of which is algoritmic and the other is analytical, have found from two different upper bound approximations. By exploiting analytical solution, a fast and low-complex algorithm is derived. At the end of paper, these two approximations and DC programming algorithm which is well-studied and given well-approximated lower bound have been compared with each other.