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This paper proposes a reduced-complexity multichannel assignment scheme for short-range cellular systems. It treats the scenario when a number of small-cell (e.g., femtocell) access points (APs) can be shared to serve active scheduled users. The APs employ isotropic antenna arrays and operate using an open-access control strategy. To improve the reuse ratio of physical resources, the APs are assumed to occupy a single physical channel, wherein coordination among them is infeasible. On the other hand, to improve the spatial coverage, a scheduled user can be served by a single transmit channel from an AP at a time. For the case of overloaded APs and when the feedback links are capacity limited, the scheme attempts to identify the suitable transmit channels from the deployed APs in an adaptive manner such that certain performance and/or processing load limits are satisfied. The effects of some system and design parameters on the outcomes of the scheme are thoroughly discussed. Novel results for the statistics of the resulting interference power are presented, from which results for some performance measures and processing loads are obtained. Numerical and simulations results are provided to clarify the achieved gains, as compared with related models under different operating conditions. [ABSTRACT FROM PUBLISHER]