On the QoS feasibility region in the vector broadcast channel

We investigate the geometry of the feasible Quality of Service (QoS) region in the vector broadcast channel when the available transmit power is unbounded. It turns out that a complete description of the feasible QoS region attains its simplest form in the minimum mean square error (MMSE) domain although most of the literature handles feasibility in the SINR domain. As our main contribution, we show that the closure of the feasible MMSE region is a polytope corresponding to a hyper-cube that maybe is cropped by an additional half-space constraint. Interestingly, this half-space constraint is the only relevant one which separates feasibility from infeasibility and it reflects a lower bound on the sum MMSE. Under the assumption of regular channels, this lower bound does not depend on the channel realization but solely depends on the number of users and antennas deployed at the base station. Testing feasibility of given QoS targets is easily performed by first converting the QoS targets into upper bounds on the MMSEs and afterwards verifying that the sum of target MMSEs is larger than the difference between antennas at the base station and the number of users. The derived results can be used to decide whether a new user with given QoS requirements can be admitted to the system, and if not, how the requirements have to be adapted such that they become feasible.