The Optimal DoF for the Noncoherent MIMO Channel with Generic Block Fading

The high-SNR capacity of the noncoherent MIMO channel has been derived for the case of independent and identically distributed (IID) Rayleigh block fading by exploiting the Gaussianity of the channel matrix. This implies the optimal degrees of freedom (DoF), i.e., the capacity pre-log factor. Nevertheless, as far as the optimal DoF is concerned, IID Rayleigh fading is apparently a sufficient but not necessary condition. In this paper, we show that the optimal DoF for the IID Rayleigh block fading channel is also the optimal DoF for a more general class of generic block fading channels, in which the random channel matrix has finite power and finite differential entropy. Our main contribution is a novel converse proof based on the duality approach.