In this work, a two-tier heterogeneous network architecture is investigated for a channel with multiple carriers. The studied system structure qualifies as a general framework that covers both heterogeneous network (HetNet) structures and cognitive radio (CR) structures. The first and second tiers can be thought as a macro-cell and a femto-cell in a HetNet, respectively. Similarly, the first and second tier users coincide with the primary and secondary users in a CR network, respectively. Unlike our previous works, the data rate maximization problem is investigated for multi-carrier scenarios. It is intended to maximize the total data rate of the second tier users under transmit power constraints per user and per frequency band and a total interference power constraint at the first tier. The performance enhancement of using multiple carriers is investigated by forming a near-optimum, analytically found upper bound for the sum data rate.