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Frequency planning is a common intercell interference (ICI) management strategy in narrowband cellular networks. In this paper, we consider an alternative approach that allows full frequency reuse in every cell and deploys a network-wide linear minimum mean square error (LMMSE) receiver as the front-end processor to suppress ICI. Assuming equal transmit power for all users, we compare the achievable rate of the LMMSE receiver in the information-theoretic sense against the rates achieved by two different frequency reuse schemes, namely the conventional reuse scheme with single-cell processing and a reuse scheme that allows interference-free processing of signals from adjacent cells. We first compare the performance under a fixed path-gain model and then extend to a random fading model.