MIMO capacity pre-log for flat fading stationary channels with no CSIR

The asymptotic capacity for the non-coherent MIMO stationary channels having n_t transmit and n_r receive antennas with flat fading is the focus of this paper. Fading processes of concern are bandlimited. These non-coherent MIMO channels were studied by Etkin and Tse and lower bound of capacity was shown to grow with min(n_t, n_r)[1 - min(n_t, n_r)mu] log(SNR) where mu is the normalized Doppler bandwidth. The contribution of this paper is to specify the pre-log for MIMO channels and this is done by giving matching upper and lower bounds of the pre-log. Moreover min(n_t, n_r) factor in the pre-log term bears a small modification. The actual pre-log is min(n_t, n_r, 1/2mu)[1 - min(n_t, n_r, 1/2mu)mu] and takes into account the optimal number of streams that should be activated as a function of the Doppler bandwidth.