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In order to address the increasing demands for high data rates in wireless communications, carrier aggregation (CA) is introduced in Long Term Evolution-Advanced (LTE-A) Release-10 for HetNets, a platform for the implementation of features with new functionalities. One of the major challenges in CA HetNets is to find an appropriate resource allocation algorithm for various nodes with different data rate requirements. Stable matching (SM) algorithm is one of the most popular allocation algorithm in the last decade. In this study, an important variation of the many-to-one SM (MSM) algorithm is proposed as partial feedback SM (PFM) algorithm, to achieve fair and stable subcarrier allocation by considering rate requirements in a HetNet. The stability concerns for CA HetNets are investigated for the proposed variation of the MSM algorithm in order to determine the rate satisfaction of both user equipments and the entire HetNet. The rate and fairness performances of the proposed algorithm are also compared with the optimal rate algorithm (ORA), which achieves the maximum rate, and with the proportional fair (PF) algorithm, which is widely used for fair resource allocation problems. Computer simulations show that the proposed variations of SM algorithms are very robust even with partial channel state information ( CSI) in terms of rate and fairness. Keywords: Stable matching Carrier aggregation HetNet Fairness. (C) 2019 Elsevier B.V. All rights reserved.