In the previous work, a single antenna interference cancellation (SAIC) algorithm named least mean square-blind joint maximum likelihood sequence estimation (LMS-BJMLSE) has been proposed. However, LMS-BJMLSE requires a long training sequence (TS) for channel estimation, which reduces the transmission efficiency. In another work, in order to solve this problem, a subcarrier identification and interpolation algorithm was proposed, in which the slowly converging subcarriers are identified by exploiting the correlation between the mean-square error (MSE) produced by LMS and the mean-square deviation (MSD) of the desired channel estimate. However, this correlation relationship was only found based on simulation results and no clear mathematical proof was given. The performance of the algorithm was only evaluated for the case of single interference. In this paper, the mathematical proof of the correlation relationship between MSE and MSD is given. Furthermore, we generalize LMS-BJMLSE from single antenna to receiver diversity, which is shown to provide a huge improvement over single antenna. The performance of LMS-BJMLSE is also evaluated for the case of dual interference.