Degrees of Freedom of Generic Block-Fading MIMO Channels Without a Priori Channel State Information

We study the high-signal-to-noise-ratio capacity of generic multiple-input multiple-output (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.