Degrees of Freedom of Generic Block-Fading MIMO Channels without A Priori Channel State Information

We studynthe high-SNR capacity of generic MIMO Rayleigh block-fading channels in the noncoherent setting where neither transmitter nor receiver has a priori channel state information but both are aware of the channel statistics. In contrast to the well-established constant block-fading model, we allow the fading to vary within each block with a temporal correlation that is "generic" (in the sense used in the interference-alignment literature). We show that the number of degrees of freedom of a generic MIMO Rayleigh block-fading channel with $T$ transmit antennas and block length $N$ is given by $T(1-1/N)$ provided that $T<N$ and the number of receive antennas is at least $T(N-1)/(N-T)$. A comparison with the constant block-fading channel (where the fading is constant within each block) shows that, for large block lengths, generic correlation increases the number of degrees of freedom by a factor of up to four.