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

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