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

We study the 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 interferencealignment 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 blockfading 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.