In this work, a two-tier heterogeneous network architecture is investigated. The proposed system structure qualifies as a general framework that covers both heterogeneous network (HetNet) structures and cognitive radio (CR) structures. The first tier and the second tier coincide with a macro-cell and a femtocell in a HetNet, respectively. Similarly, the first tier users and the second tier users correspond to the primary users and secondary users in a CR network, respectively. In our previous works, it was assumed that the channel state information of all users is perfectly available at the second tier base station. However, having perfect channel state information becomes impractical with increased number of users. In order to prevent this, the data rate maximization problem is investigated under feedback constraints. It is intended to maximize the total data rate of the second tier users under a total interference power constraint at the first tier and also under various feedback constraints. Because of the feedback constraint, a decrease on the overall system performance occurs. Different feedback scenarios are investigated in order to examine and remedy the reduction on the performance.