Geometric characterization of capacity-constraint function

Maximizing the mutual information under a linear input constraint is considered from a geometric point of view. Assuming a suitable regularity condition on the channel matrix, it is found that the probability distribution (PD) equidistant from the row PDs of the channel matrix plays an important role, and the maximum is achieved by the projection of that PD onto the set of PDs satisfying the constraint. The PD attaining the capacity-constraint function is obtained by using Lagrange´s method of indeterminate coefficients at most (m-2) times