  In this paper, we study upper bounds on the sum capacity of the downlink
multicell processing model with finite backhaul capacity for the simple case of
2 base stations and 2 mobile users. It is modelled as a two-user multiple
access diamond channel. It consists of a first hop from the central processor
to the base stations via orthogonal links of finite capacity, and the second
hop from the base stations to the mobile users via a Gaussian interference
channel. The converse is derived using the converse tools of the multiple
access diamond channel and that of the Gaussian MIMO broadcast channel. Through
numerical results, it is shown that our upper bound improves upon the existing
upper bound greatly in the medium backhaul capacity range, and as a result, the
gap between the upper bounds and the sum rate of the time-sharing of the known
achievable schemes is significantly reduced.
