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In this paper synchronization of uncoordinated OFDM spectrum sharing systems that operate in the presence of narrowband interference (NBI) is analyzed. Conventional synchronization algorithms based on correlation of synchronization preamble in time domain suffer from considerable performance degradation when NBI is present. To overcome this degradation we propose and analyze a method to detect NBI presence and to suppress its influence on synchronization before estimation of synchronization parameters is performed at the OFDM receiver. We focus on an OFDM WLAN system operating in license-exempt band and analyze synchronization performance when NBI is active. The proposed method does not introduce any additional preamble overhead with respect to existing WLAN preamble and requires only slightly higher computational complexity at the receiver. To illustrate effectiveness of the proposed method, several numerical examples are provided.