Wireless communication systems often suffer problems from multipath and interfering signals. This paper compares two types of adaptive beamforming algorithms for optimising and setting the weights of smart antenna systems, namely the Least Mean Square algorithm (LMS) and Sample Matrix Inversion (SIM). The direction of the main beam of the antenna system is adjusted to enhance the desired signal, while interfering signals are mitigated by having nulls pointed in their directions. The mathematical formulations and necessary conditions for the above algorithms are derived and verified by numerical examples, with overall behaviour obtained by MATLAB simulation. Performance evaluations are made for different cases of arrival angles, and in conclusion, the advantages and disadvantages of each algorithm are presented.