Sound field reproduction is a physical approach to the reproduction of the natural spatial character of hearing. It is also useful in experimental acoustics and psychoacoustics. Wave field synthesis (WFS) is a known open-loop technology which assumes that the reproduction environment is anechoic. A real reflective reproduction space thus reduces the objective accuracy of WFS. Recently, adaptive wave field synthesis (AWFS) was defined as a combination of WFS and active compensation. AWFS is based on the minimization of reproduction errors and on the penalization of departure from the WFS solution. This paper focuses on signal processing for AWFS. A classical adaptive algorithm is modified for AWFS: filtered-reference least-mean-square. This modified algorithm and the classical equivalent leaky algorithm have similar convergence properties except that the WFS solution influences the adaptation rule of the modified algorithm. The paper also introduces signal processing for independent radiation mode control of AWFS on the basis of plant decoupling. Simulation results for AWFS are introduced for free-field and reflective spaces. The two algorithms effectively reproduce the sound field and compensate for the reproduction errors at the error sensors. The independent radiation mode control allows a more flexible tuning of the algorithm.