  We consider multi-antenna base stations using orthogonal frequency-division
multiple access (OFDMA) and space division multiple access (SDMA) techniques to
serve single antenna users, where some of those users have minimum rate
requirements and must be served in the current time slot (real time users),
while others do not have strict timing constraints (non real time users) and
are served on a best effort basis. The resource allocation problem is to find
the user assignment to subcarriers and the transmit beamforming vectors that
maximize a linear utility function of the user rates subject to power and
minimum rate constraints. The exact optimal solution to this problem can not be
reasonably obtained for practical parameters values of the communication
system. We thus derive a dual problem formulation whose optimal solution
provides an upper bound to all feasible solutions and can be used to benchmark
the performance of any heuristic method used to solve this problem. We also
derive from this dual optimal solution a primal-feasible dual-based method to
solve the problem and we compare its performance and computation time against a
standard weight adjustment method. We find that our method follows the dual
optimal bound more closely than the weight adjustment method. This off-line
algorithm can serve as the basis to develop more efficient heuristic methods.
