  With the goal of optimizing the CM capacity of a finite constellation over a
Rayleigh fading channel, we construct for all dimensions which are a power of 2
families of rotation matrices which optimize a certain objective function
controlling the CM capacity. Our construction does not depend on any
assumptions about the constellation, dimension, or signal-to-noise ratio. We
confirm the benefits of our construction for uniform and non-uniform
constellations at a large range of SNR values through numerous simulations. We
show that in two and four dimensions one can obtain a further potential
increase in CM capacity by jointly considering non-uniform and rotated
constellations.
