ABSTRACTMost of the recent and emerging wireless systems have selected orthogonal frequency division multiplexing (OFDM) scheme as the basis for the physical layer due to its flexibility and robustness. OFDM is commonly considered also as the first candidate technology for advanced cognitive radio, dynamic spectrum use and fragmented coexistence scenarios, including the 5G system development. Nevertheless, OFDM has the problem of high‐power spectral sidelobes around the active subcarriers, which limit its feasibility in fragmented spectrum use and asynchronous frequency division multiple access operation. Therefore, various sidelobe suppression techniques have been proposed in the literature to mitigate these effects. This paper investigates four different suppression techniques: time‐domain windowing, cancellation carrier method, subcarrier weighting and polynomial cancellation coding, as well as their combinations. These methods are elaborated for a practical heterogeneous fragmented spectrum use scenario based on 5‐MHz 3GPP Long‐Term Evolution (LTE), proposing various enhancements to achieve effective suppression in narrow gaps with affordable complexity. In addition to the spectral characteristics, also, the possible side effects are evaluated in details, considering peak‐to‐average power ratio characteristics, error rate performance, computational complexity and resources usage. Copyright © 2014 John Wiley & Sons, Ltd.