The authors investigate several adaptive noise-cancellation algorithms and their effectiveness in improving the quality of speech degraded by additive acoustic noise in mobile communications. A personal-computer system which was used to acquire test data and implement the algorithms is described. The algorithms studied include least mean squares (LMS), recursive least squares (RLS), a fast transversal filter (FTF) implementation of RLS, direct solution of the normal equation, and an adaptive notch filter. The results of a comparison of the algorithms based on various criteria are presented. The results of applying each of the algorithms to adaptive noise cancellation in mobile environments are described and evaluated. The FTF algorithm demonstrated excellent convergence qualities compared to the LMS algorithm.