In this paper, we investigate resource allocation in the multicarrier spread spectrum systems, especially in the multicell downlink multicarrier direct‐sequence code division multiple‐access systems. The allocation of resources including subcarriers and spreading codes aims to maximize the system reliability, thereby resulting in the high‐reliability mutlicarrier systems. For the sake of achieving low complexity, we develop the novel resource allocation framework. We propose two resource allocation algorithms, which are the simplified heuristic subcarrier‐ and code‐allocation (SHSC) algorithm and the enhanced heuristic subcarrier‐ and code‐allocation (EHSC) algorithm. The two proposed algorithms can find the promising suboptimum solutions to the mixed integer nonconvex resource allocation problem. The SHSC algorithm has lower complexity and demands less backhaul resources than the EHSC algorithm. In return, the EHSC algorithm performs better than the SHSC algorithm. Nevertheless, we show that both algorithms significantly outperform the existing algorithms while approaching the optimal algorithm of high complexity.