  We consider the downlink of a multi-cell system with multi-antenna base
stations and single-antenna user terminals, arbitrary base station cooperation
clusters, distance-dependent propagation pathloss, and general "fairness"
requirements. Base stations in the same cooperation cluster employ joint
transmission with linear zero-forcing beamforming, subject to sum or per-base
station power constraints. Inter-cluster interference is treated as noise at
the user terminals. Analytic expressions for the system spectral efficiency are
found in the large-system limit where both the numbers of users and antennas
per base station tend to infinity with a given ratio. In particular, for the
per-base station power constraint, we find new results in random matrix theory,
yielding the squared Frobenius norm of submatrices of the Moore-Penrose
pseudo-inverse for the structured non-i.i.d. channel matrix resulting from the
cooperation cluster, user distribution, and path-loss coefficients. The
analysis is extended to the case of non-ideal Channel State Information at the
Transmitters (CSIT) obtained through explicit downlink channel training and
uplink feedback. Specifically, our results illuminate the trade-off between the
benefit of a larger number of cooperating antennas and the cost of estimating
higher-dimensional channel vectors. Furthermore, our analysis leads to a new
simplified downlink scheduling scheme that pre-selects the users according to
probabilities obtained from the large-system results, depending on the desired
fairness criterion. The proposed scheme performs close to the optimal
(finite-dimensional) opportunistic user selection while requiring significantly
less channel state feedback, since only a small fraction of pre-selected users
must feed back their channel state information.
