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In recent years, the family of multicarrier code-division multiple-access (MC-CDMA) transmission technologies has drawn a lot of attention in providing broadband wireless communication services. From the literature, one can find extensive discussions in many aspects of MC-CDMA under a flat system architecture either for conventional or currently emerging cognitive radio (CR) systems. In this paper, we shift the focus from the flat architecture to the hierarchical architecture based on 2-D-spread multicarrier direct-sequenced CDMA, in which a microcell is embedded in the primitive macrocell. However, in such a hierarchical architecture, severe intercell interference can occur between the macrocell and the microcell. Via the interference avoidance code assignment strategy, this kind of intercell interference in downlink transmissions can be eliminated. To this end, we define the white, gray, and black spreading codes to facilitate the management of spreading code resources. Properly allocating the white and gray spreading codes but the black ones can achieve a higher spectrum efficiency without harming the macrocell users. For the purpose of evaluating the candidacy of the gray spreading codes, a sophisticated interference analysis is conducted to define a new multiple access interference (MAI) coefficient to quantize the amount of interference imposed on a microcell user. With the help of the new MAI coefficient, a less-interfered white or gray spreading code can be assigned to microcell users, which can bring about an extra 55% of call admissions in one of our considered cases. Moreover, the capability of the proposed hierarchical system architecture, as well as the interference management scheme for developing the femtocell system, has also been proved via simulation results with a large number of femtocells. It is believed that by cooperating with the substream deactivation technique, the proposed spreading code management associated with the hierarchical system - rchitecture can be a potential prototype of the CR-based femtocell system.