Speech signal enhancement is an important topic in speech processing where signal changes its characteristics with time depending on various conditions. An important problem that affects the signal enhancement is the background noise which is a major source of quality degradation in speech and audio signals. Adaptive noise cancellation algorithms are used to reduce this noise with relatively fast convergence as desired. Minimization techniques like LMS, NLMS and RLS are widely used due to its simplicity in computation and implementation. These algorithms are evaluated under several conditions like sensitivity for language, text gender and noise power. Certain parameters were designed to obtain the best performance under various conditions where the RLS algorithm has outperformed the other two algorithms when noise power is fixed and that noise power has more influence on the RLS algorithm.