The main purpose of this article is to evaluate and to compare the performance metrics, array factor (AF), signal to interference plus noise ratio (SINR), mean square error (MSE), bit error rate (BER), and also computational complexity of different modified blind adaptive BEAMFORMING algorithms based on constrained constant modulus (CCM).Two modified algorithms use adaptive step size mechanisms in the stochastic gradient (SG) algorithm for adjusting the step size. The third one, CCM-RLS, uses recursive least squares (RLS) optimization algorithm which is replaced by the inverse correlation matrix instead of the step size. In the case of a uniform linear array (ULA) and 5 users, one as desired signal and the others as interference signals, simulation results show that the modified algorithms, CCMRLS, CCM-SG-time averaging adaptive step size (TAASS) and CCM-SG-modified adaptive step size (MASS), offer higher performance with respect to conventional CCM-SG, respectively. Comparing the performance of CCM-RLS and adaptive step size versions of CCM-SG show that CCM-RLS converges faster and it can cancel the interferences close to the desired signal, more effectively. Moreover, the resulting SINR level is higher and BER is less than the other methods.However, CCM-SG-MASS and CCM-SG-TAASS have less computational complexity, additions and multiplications.