  We study the converse and achievability for the degrees of freedom of the
multicellular multiple-input multiple-output (MIMO) multiple access channel
(MAC) with constant channel coefficients. We assume L>1 homogeneous cells with
K>0 users per cell where the users have M antennas and the base stations are
equipped with N antennas. The degrees of freedom outer bound for this L-cell
and K-user MIMO MAC is formulated. The characterized outer bound uses insight
from a limit on the total degrees of freedom for the L-cell heterogeneous MIMO
network. We also show through an example that a scheme selecting a transmitter
and performing partial message sharing outperforms a multiple distributed
transmission strategy in terms of the total degrees of freedom. Simple linear
schemes attaining the outer bound (i.e., those achieving the optimal degrees of
freedom) are explores for a few cases. The conditions for the required spatial
dimensions attaining the optimal degrees of freedom are characterized in terms
of K, L, and the number of transmit streams. The optimal degrees of freedom for
the two-cell MIMO MAC are examined by using transmit zero forcing and null
space interference alignment and subsequently, simple receive zero forcing is
shown to provide the optimal degrees of freedom for L>1. By the uplink and
downlink duality, the degrees of freedom results in this paper are also
applicable to the downlink. In the downlink scenario, we study the degrees of
freedom of L-cell MIMO interference channel exploring multiuser diversity.
Strong convergence modes of the instantaneous degrees of freedom as the number
of users increases are characterized.
