This paper investigates the allocation of resources, including subcarriers and spreading codes, as well as intercell interference (ICI) mitigation for multicell downlink multicarrier direct-sequence code division multiple-access systems, which aim to maximize the system's spectral efficiency (SE). The analytical benchmark scheme for resource allocation and ICI mitigation is derived by solving or closely solving a series of mixed integer non-convex optimization problems. Based on the optimization objectives the same as the benchmark scheme, we propose a novel distributed resource allocation assisted by ICI mitigation scheme referred to as resource allocation assisted by ICI mitigation (RAIM), which requires very low implementation complexity and demands little backhaul resource. Our RAIM algorithm is a fully distributed algorithm, which consists of the subcarrier allocation (SA) algorithm named RAIM-SA, spreading code allocation (CA) algorithm called RAIM-CA and the ICI mitigation algorithm termed RAIM-IM. The advantages of the RAIM are that its CA only requires limited binary ICI information of intracell channels, and it is able to make mitigation decisions without any knowledge of ICI information. Our simulation results show that the proposed RAIM scheme, with very low complexity required, achieves significantly better SE performance than other existing schemes, and its performance is very close to that obtained by the benchmark scheme.