In this letter, we propose a modified version of Fast Independent Component Analysis (FICA) algorithm to solve the self-interference cancellation (SIC) problem in In-band Full Duplex (IBFD) communication systems. The complex mixing problem is mathematically formulated to suit the real-valued blind source separation (BSS) algorithms. In addition, we propose a method to estimate the ambiguity factors associated with ICA lumped together with the channels and residual separation error. Experiments were performed on an FD platform where FICA-based BSS was applied for SIC in the frequency domain. Experimental results show superior performance compared to least squares SIC by up to 6 dB gain in the SNR.