In previous works, a blind single antenna interference cancellation (SAIC) algorithm named least mean square-blind joint maximum likelihood sequence estimation (LMS-BJMLSE) has been proposed for OFDM systems. It is blind with respect to interference and is able to cancel interference by only one receive antenna. However, LMS-BJMLSE requires a long training sequence (TS) for channel estimation, which greatly reduces the transmission efficiency. Furthermore, since TS is not available in 4G LTE systems, LMS-BJMLSE can not be applied directly. In this paper, in order to solve this problem, a SINR and symbol position weight adaptive algorithm is proposed, and named as adaptive LMS-BJMLSE (ALMS-BJMLSE). For each slot, ALMS-BJMLSE dynamically decides the number of antennas used for interference cancellation and adjusts the step size, based on estimated SINR conditions and symbol position weight. Simulation results demonstrate that ALMS-BJMLSE achieves a much better balance between performance and transmission efficiency compared to the conventional LMS-BJMLSE algorithm, and can be applied for 4G LTE systems.