Fisher information decision directed discrete optimisation

Finite alphabet optimisation problems occur in many fields of engineering, including wireless communications and blind source separation. An optimal solution through exhaustive search is often computationally intractable, so sub-optimal solutions are employed. One popular approach is simply to round each element of the unconstrained solution to the nearest member of the known alphabet. The paper presents a novel approach which has better error performance than rounding but with only a moderate increase in complexity. The method uses Fisher information to determine the order in which optimisation is carried out. The inverse of the Fisher information matrix indicates which element of the estimate is, on average, most likely to have the smallest error. Thus the first element to be optimised is the one most likely to be correct. This then improves the likelihood of subsequent elements being correct. The method is developed and an example is included of its application to the discrete blind source separation problem.